I 


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1 

Form  L-9-15i)(-8,'24 

WENTWORTH-SMITH  MATHEMATICAL  SERIES 


ORAL  ARITHMETIC 


BY 

2zBo  3 

GEORGE  WENTWORTH 


DAVID  EUGENE  SMITH 


GINN  AND  COMPANY 

BOSTON  •  NEW  YORK  •  CHICAGO  •  LONDON 


ENTERED  AT  STATIONERS'  HALL 


COPYRIGHT,  1910,  BY 
GEORGE  WENTWORTH  AND  DAVID  EUGENE  SMITH 


ALL  RIGHTS  RESERVED 
910.7 


Cbt   gtbtnaum 

GINN  AND  COMPANY  •  PRO- 
PRIETORS •  BOSTON  •  U.S.A. 


Q  A 


PREFACE 

Ever  since  Warren  Colburn,  following  in  the  footsteps 
of  Pestalozzi,  published  his  Intellectual  Arithmetic  early  in 
the  last  century,  teachers  have  recognized  the  great  value 
of  oral  work  in  number.  Oral  work  is  furnished  in  the  text- 
books in  primary  arithmetic,  and  in  some  cases  in  books 
for  higher  grades.  Most  text-books  used  in  the  last  four 
years  of  the  elementary  school,  however,  need  supplement- 
ing in  this  important  particular,  and  this  reason  prompted 
the  authors  to  prepare  this  book. 

The  chief  principles  that  have  guided  the  selection  and 
arrangement  of  material  have  been  as  follows :  The  oral 
arithmetic  needed  for  practical  life  relates  mainly  to  the 
fundamental  operations.  These  operations  should,  there- 
fore, be  reviewed  in  each  school  year,  the  degree  of  diffi- 
culty increasing  slightly  as  the  pupil  proceeds,  but  never 
becoming  greater  than  that  encountered  in  daily  business 
life.  Together  with  the  work  in  abstract  number,  which 
Festalozzi  so  strongly  emphasized,  should  go  a  range  of 
applications  related  to  the  pupil's  interests  as  they  vary 
from  year  to  year.  No  particular  effort  should  be  made  to 
conform  to  the  sequence  of  any  text-book  in  written  arith- 
metic, since  the  pEime^object  of  oral  arithmetic  is  contin- 
ually to  review  topics  that  have  been  passed  in  the  usual 
sequence  of  written  work. 

The  effectiveness  of  oral  arithmetic  demands  that  this 
work  should  form  part  of  every  recitation,  or  at  least  of 


vi  PREFACE 

every  other  recitation.  A  text-book  upon  this  subject,  there- 
fore, serves  its  purpose  best  when  arranged  in  four  chapters 
for  the  last  four  years  of  the  elementary  school,  each  chap- 
ter being  divided  into  a  hundred  exercises,  thus  allowing 
about  a  half  exercise  for  each  day,  or  a  whole  exercise  for 
every  second  day. 

Teachers  are  advised  to  accustom  their  pupils  from  the 
beginning  to  rapid,  sprightly,  crisp  responses.  Such  a  habit 
will  soon  result  in  a  mental  alertness  in  number  work  that 
not  only  will  be  valuable  in  after  life,  but  will  react  very 
favorably  upon  the  work  in  ordinary  written  arithmetic. 
Teachers  will  naturally  make  such  a  rearrangement  of  the 
exercises  as  seems  best,  particularly  in  the  last  chapter,  and 
will  supplement  the  applied  problems  with  others  relating 
to  local  customs  and  industries. 

The  best  results  are  obtained  with  any  oral  arithmetic 
by  introducing  the  book  in  the  class  for  which  the  first 
chapter  is  written.  It  may,  however,  be  introduced  at  a 
later  period,  provided  a  sufficient  review  of  the  earlier 
work  is  undertaken  to  accustom  the  pupils  to  rapid  mental 
work.  In  general,  the  problems  are  of  such  a  nature  that 
all  the  work  can  easily  be  done  mentally  if  the  preceding 
exercises  have  been  taken;  but,  as  is  always  the  case  in 
oral  arithmetic,  the  teacher  will  find  it  advisable  occasion- 
ally to  write  some  of  the  numbers  on  the  blackboard,  par- 
ticularly if  cancellation  is  involved. 

Any  corrections  or  suggestions  relating  to  the  book  will 

be  thankfully  received. 

GEORGE  WENTWORTH 
DAVID  EUGENE  SMITH 


CONTENTS 


CHAPTER  I 

SECTION  PAGE 

I.   OPERATIONS  WITH  INTEGERS 1 

II.    COMMON  FRACTIONS 25 

III.  ALIQUOT  PARTS 42 

IV.  DENOMINATE  NUMBERS 44 

CHAPTER  II 

I.    OPERATIONS  WITH  INTEGERS 55 

II.    SHORT  METHODS 73 

III.  COMMON  FRACTIONS 82 

IV.  DECIMAL  FRACTIONS 94 

V.    DENOMINATE  NUMBERS 104 

CHAPTER  III 

I.    FUNDAMENTAL  OPERATIONS 109 

II.    MEASURES 123 

III.  LONGITUDE  AND  TIME 135 

IV.  PERCENTAGE 138 

V.    RATIO  AND  PROPORTION 163 

CHAPTER  IV 

""  I.   FUNDAMENTAL  OPERATIONS.    BUSINESS  PROBLEMS  167 

II.   EXCHANGE 184 

III.  METRIC  SYSTEM 189 

IV.  TAXES 194 

V.    INSURANCE 196 

VI.    CORPORATIONS 198 

VII.  POWERS  AND  ROOTS 202 

VIII.    MENSURATION 206 

vii 


ORAL  ARITHMETIC 


CHAPTER  I 
2.2  SO  S 
OPERATIONS  WITH  INTEGERS 

1.   Adding  2's  and  3's 


1.  12  +  2. 
2.  15  +  2. 
3.  18  +  2. 
4.  24  +  2. 

5.  26  +  2. 

6.  23  +  2. 
7.  27  +  2. 
8.  19  +  2. 

9.  42  +  3. 
10.  18  +  3. 
11.  17+3. 
12.  34  +  3. 

13.  26  +  3. 

14.  33  +  3. 
15.  35  +  3. 
16.  19  +  3. 

17.  How  much  is  $17  and  $3?    19  ft.  and  3  ft.  ?    18yd. 
and  3  yd.  ? 

18.  How  much  is  $19  and  $2  ?     $12  and  $9  ?     9  +  2  ? 

2  +  9? 

19.  How  much  is  $29  and  $3  ?     $23  and  $9  ?     9  +  3  ? 

3  +  9? 

2.   Adding  4's  and  5's 


1.  22  +  4. 
2.  36  +  4. 
3.  44  +  4. 
4.  58  +  4. 

5.  65  +  4. 
6.  73  +  4. 

7.  77  +  4. 
8.  89  +  4. 

9.  36  +  5. 
10.  44  +  5. 
11.  58  +  5. 
12.  65  +  5. 

13.  72  +  5. 
14.  77  +  5. 
15.  83  +  5. 
16.  89  +  5. 

17.  How  much  is  $76  and  $4  ?    88  ft.  and  4  ft.  ?    77  bu. 
and  4  bu.  ? 

18.  How  much  is  $76  and  $5  ?    37  in.  and  5  in.  ?    88  yd. 
and  5  yd.  ? 

19.  How  much  is  $89  and  $5  ?     $85  and  $9  ?     9  +  5  ? 
5  +  9? 

1 


INTEGERS 
3.   Adding  6's  and  7's 


1.  54  +  6. 
2.  66  +  6. 
3.  73  +  6. 
4.  88  +  6. 

5.  92  +  6. 
6.  77  +  6. 
7.  75  +  6. 
8.  99  +  6. 

9.  43  +  7. 

10.  86  +  7. 
11.  78  +  7. 
12.  77  +  7. 

13.  64  +  7. 
14.  32  +  7. 
15.  75  +  7. 
16.  99  +  7. 

17.  How  much  is  $27  and  $6  ?    38  ft.  and  6  ft.  ? 

18.  How  much  is  42  mi.  and  7  mi.  ?    68/  and  7/  ? 

19.  How  much  is  67/  and  6/  ?    65/  and  7/  ?    28  sq.  in. 
and  6  sq.  in.  ? 

20.  If  you  have  37  marbles  and  buy  7  more,  how  many 
will  you  then  have  ? 

;    21.  If  a  grocer  has  87  bbl.  of  flour  and  buys  7  more,  how 
many  will  he  then  have  ? 

22.  If  a  farmer  has  46  head  of  cattle  and  buys  half  a 
dozen  more,  how  many  will  he  then  have  ? 

4.   Adding  8's  and  9's 


1.  24  +  8. 

2.  26  +  8. 
3.  23  +  8. 
4.  38  +  8. 

5.  35  +  8. 
6.  27  +  8. 
7.  92  +  8. 
8.  99  +  8. 

9.  23  +  9. 
10.  36  +  9. 
11.  35  +  9. 
12.  48  +  9. 

13.  37  +  9. 
14.  54  +  9. 
15.  92  +  9. 
16.  99  +  9. 

17.  How  much  is  $68  and  $8  ?    $107  and  $8  ? 

18.  How  much  is  $33  and  $9  ?     $106  and  $9  ?     $199 
and  $9? 

19.  Which,  if  either,  is  greater,  $108  +  $9,  or  $109  +  $8? 
State  the  sums. 

20.  If  a  man  pays  $23  for  a  saddle  and  $8  for  a  bridle, 
how  much  does  he  pay  for  both  ? 

21.  If  a  man  has  a  farm  of  166  acres  and  buys  9  acres 
more,  how  much  does  he  then  have  ? 

22.  The  three  sides  of  a  triangle  are  9  ft.,  7  ft.,  and  8  ft. 
What  is  the  sum  of  the  sides  of  the  triangle  ? 


ADDITION 
5.   Miscellaneous  Addition 


1.  15  +  7. 
2.  17  +  4. 
3.  16  +  8. 
4.  19  +  9. 

5.  27  +  3. 
6.  48  +  2. 
7.  56  +  4. 
8.  73  +  7. 

9.  26  +  5. 
10.  34  +  8. 
11.  47  +  5. 
12.  58  +  3. 

13.  39  +  5. 
14.  94  +  3. 
15.  83  +  8. 
16.  95  +  6. 

17.  How  much  is  55/  and  7/?    57/  and  5/? 

18.  How  much  is  69  ft.  and  7  ft.?     67  ft.  and  9  ft.  ? 

19.  How  much  is  $138  and  $4  ?    $134  and  $8  ? 

20.  How  much  is  54  acres  and  9  acres  ?    98  acres  and 

4  acres  ? 

vJ21.  The  four  sides  of  a  flower  bed  are  4  ft.,  2  ft.,  4  ft., 

5  ft.    What  is  the  perimeter  ? 

^-22.  A  man  weighing  158  Ib.  is  carrying  a  basket  that 
weighs  3  Ib.  in  which  there  are  9  Ib.  of  groceries.  What 
is  the  combined  weight  of  all  three  ? 

6.   Miscellaneous  Addition 

1.  52  +  9.  5.  56  +  6.  9.  85  +  5.  13.  97  +  9. 

2.  83  +  9.  6.  97  +  7.  10.  67  +  6.  14.   69  +  8. 

3.  94  +  6.  ,   7.  98  +  8.  11.  68  +  8.  15.  49  +  7. 

4.  75  +  8.  '  8.  45  +  6.  12.  98  +  6.  16.  98  +  5. 

17.  Add  $78  and  $5;  $75  and  $8  ;  5  and  8;  8  and  5. 

18.  Add  59^  and  4/;  54^  and  9/ ;  9  and  4  ;  4  and  9. 

19.  Add  77/  and  7/;  88  /  and  8/;  7  and  7 ;  8  and  8. 

20.  How  much  is  86  ft.  and  9  ft.  ?    56  yd.  and  9  yd.  ? 
96  and  9  ? 

21.  How  much  is  16  in.  and  8  in.  ?    $76  and  $8  ?    $9 
and  $6? 

22.  If  you  buy  groceries  weighing  31  Ib.,  5  Ib.,  and  9  Ib., 
what  is  the  total  weight  ? 

23.  If  you  spend  37/,  8/,  and  5/,  how  much  do  you 
spend  in  all  ? 


4  INTEGERS 

7.   Adding  Two-figure  Numbers 

Think  of  25  +  17  as  25  +  10  +  7,  and  then  as  35  +  7.    State  aloud 
only  the  result,  42. 

1.  30  +  10.  5.  26  +  10.  9.  29  +  10.  13.  32  +  10. 

2.  30  +  17.  6.  26  +  14.  10.  29  +  12.  14.  32  +  17. 

3.  23  +  10.  7.  28  +  10.  11.  27+10.  15.  45  +  10. 

4.  23  +  15.  8.  28  +  13.  12.  27  +  18.  16.  45  +  15. 

17.  How  much  is  24/  and  15/  ?    35/  and  18/?    48/ 
and  15/? 

18.  If  you  buy  36/  worth  of  sugar  and  18X  worth  of 
fruit,  what  is  the  total  cost  ? 

19.  If  a  pony  costs  $85  and  a  saddle  costs  $17,  how 
much  do  both  cost  ? 

20.  A  boy  has  a  fishing  rod  that  cost  $3.25  and  a  line 
that  cost  18/.    How  much  did  both  cost? 

8.   Adding  Larger  Two-figure  Numbers 

Think  of  38  +  24  as  38  +  20  +  4,  or  58  +  4,  as  in  Exercise  7  above. 
State  aloud  only  the  result,  62. 

1.  30  +  20.  .5.  30  +  40.  9.  40  +  20.  13.  50  +  10. 

2.  38  +  20.  6.  37+40.  10.  44  +  20.  14.  58  +  10. 

3.  38  +  26.  7.  37  +  42.  11.  44  +  24.  15.  58  +  12. 

4.  38  +  27.  8.  37  +  44.  12.  44  +  29.  16.  58  +  15. 

17.  How  much  is  $24  and  $14  ?    $24  and  $17  ? 

18.  How  much  is  35/  and  22/?    35  /  and  28/?    48/ 
and  17/  ? 

19.  If  your  bill  at  the  grocer's  is  45/  and  27/,  what  is 
the  total  ? 

20.  If  a  man  paid  35/  for  his  railway  ticket  and  18/  for 
his  son's,  how  much  did  he  pay  for  both  ? 

21.  If  a  lady  paid  $1.05  for  some  cloth  and  75/  for  some 
ribbon,  how  much  did  she  pay  for  both  ? 


ADDITION 
9.   Adding  Larger  Two-figure  Numbers 


1. 

70  + 

20. 

5. 

80  + 

20. 

9. 

90  + 

70. 

13. 

70 

+  60. 

2. 

70  + 

30. 

6. 

85  + 

20. 

10. 

.90  + 

72. 

14. 

77 

+  60. 

3. 

73  + 

30. 

7. 

85  + 

23. 

11. 

92  + 

72. 

15. 

77 

+  63. 

4. 

73  + 

34. 

8. 

85  + 

25. 

12. 

92  + 

78. 

16. 

77 

+  67. 

17.  How  much  is  40/  and  30/  ?    47  /  and  30/? 

18.  How  much  is  80/  and  50/  ?    84  /  and  50/  ?    84/ 
and  58/  ? 

19.  If  you  give  a  boy  a  start  of  15  yd.  in  a  race,  and  over- 
take him  after  he  has  run  98  yd.,  how  far  have  you  run  ? 

20.  If  a  boy  has  235  ft.  of  kite  string  and  ties  on  45  ft. 
more,  how  many  feet  does  he  then  have  ? 

21.  If  a  certain  village  had  a  population  of  2075  five 
years   ago,   and   has   gained  87   since  then,  what   is   the 
present  population  of  the  village  ? 

10.   Adding  Larger  Two-figure  Numbers 

1.  80  +  20.  5.  80  +  40.  9.  70  +  50.  13.  90  +  20. 

2.  87  +  20.  6.  83  +  40.  10.  74  +  50.  14.  98  +  20. 

3.  87  +  23.  7.  83  +  49.  11.  74  +  56.  15.  98  +  27. 

4.  87  +  28.  8.  84  +  46.  12.  78  +  51.  16.  98  +  29. 

17.  Add  74  ft.  and  36  ft. ;  83  in.  and  27  in. ;  $75  and  $27. 

18.  Add  86  in. and  34  in. ;  92  bu.  and  38  bu. ;  $94  and  $36. 

19.  Add  $96  and  $80;    $96  and  $82;   $96  and  $87. 

20.  The  three  sides  of  a  triangle  are  23  in.,  19  in.,  and 
17  in.    What  is  the  sum  of  the  sides  of  the  triangle  ? 

21.  A  boy  weighs  67  Ib.  and  his  dog  weighs  28  Ib.  What 
do  the  two  together  weigh  ? 

22.  If  there  are  39  pupils  in  one  class  and  26  in  another, 
how  many  are  there  in  both  classes  ? 

23.  If  a  man  pays  $155  for  a  horse  and  $35  for  a  harness, 
how  much  does  he  pay  for  both  ? 


INTEGERS 
11.   Subtraction.    No  Reduction 


1. 

17 

-3. 

5. 

48 

—  7. 

9. 

33 

-10. 

13. 

58 

-11. 

2. 

26 

-4. 

6. 

59 

-8. 

10. 

48 

-10. 

14. 

66 

-11. 

3. 

78 

-5. 

7. 

29 

-9. 

11. 

23 

-10. 

15. 

78 

-11. 

4. 

39 

-6. 

8. 

42 

-  10. 

12. 

45 

-10. 

16. 

89 

-11. 

17.  From  $65  take  $12. 

18.  From  the  sum  of  $17  and  $25  take  $2. 

19.  How  much  more  is  27  than  6  ?    than  3  ? 

20.  How  much  less  is  7  than  39  ?    than  48  ?    than  97  ? 

21.  What  number  must  be  added  to  8  to  make  49  ?    to 
make  58  ? 

22.  What  number  must  be  subtracted  from  37  to  leave 
11  ?  to  leave  26  ? 

23.  If  a  boy  has  75  yd.  of  kite  string  and  loses  11  yd., 
how  much  has  he  left  ?    How  much  if  he  loses  11  yd.  more  ? 

12.    Subtraction.    No  Reduction 


1. 

37 

-10. 

5. 

52 

-10. 

9. 

52- 

11. 

13. 

37 

-11. 

2. 

28 

-10. 

6. 

87 

-10. 

10. 

34- 

11. 

14. 

49 

-  11. 

3. 

43 

-10. 

7. 

58 

-10. 

11. 

57- 

11.' 

15. 

73 

—  11. 

4. 

35 

-10. 

8. 

69 

-10. 

12. 

65- 

11. 

16. 

99 

-  11. 

17.  From  $78  take  the  sum  of  $10  and  $7. 

18.  If  a  man  buys  a  bicycle  for  $35  and  pays  $12  down, 
how  much  is  still  due  ? 

19.  It  is  42  mi.  to  a  certain  place.    How  far  is  it  to  a 
place  10  mi.  this  side  of  it  ? 

20.  If  a  boy  picks  23  qt.  of  berries  and  sells  11  qt.,  how 
many  has  he  left  ? 

21.  If  there  are  24  pupils  in  a  class  and  11  are  boys,  how 
many  are  girls  ? 

22.  If  a  man  pays  $125  for  one  horse  and  $10  less  for 
another,  how  much  does  he  pay  for  the  second  ? 


SUBTRACTION 
13.   Minuend  ending  in  0  or  1 


1. 

20 

-  9. 

5. 

40 

-4. 

9. 

21 

-4. 

13. 

51 

-5. 

2. 

50 

-3. 

6. 

30 

-6. 

10. 

41 

-9. 

14. 

31 

0 

-*™  '  —  . 

3. 

40 

-2. 

7. 

20 

-8. 

11. 

31 

-3. 

15. 

51 

-8. 

4. 

60 

-5. 

8. 

40 

—  7. 

12. 

71 

-6. 

16. 

21 

-7. 

17.  If  you  have  20/  and  spend  6/,  how  much  have  you 
left? 

18.  What  number  must  be  added  to  3  to  make  30  ?    to 
make  41? 

19.  If  you  have  gained  9  Ib.  in  a  year  and  now  weigh 
71  Ib.,  how  much  did  you  weigh  a  year  ago  ? 

^20.  If  a  man  has  to  drive  21  mi.,  how  much  farther  must 
he  go  after  he  has  driven  7  mi.  ? 

21.  A  man  having  48  head  of  cattle  bought  13  more.    He 
then  sold  8.    How  many  cattle  did  he  then  have  ? 

14.   Minuend  ending  in  2  or  3 


1.  42  -  4. 
2.  32  -  6. 
3.  22  -  3. 

4.  82  -  8. 

5.  32  -  2. 
6.  62-5. 
7.  72-9. 
8.  52-7. 

9.  23-6. 
10.  43-4. 
11.  33-3. 
12.  23-2. 

13.  33-5. 
14.  73-9- 
15.  43  _  7. 

16.  63  -  8. 

17.  If  a  class  numbers  32,  and  4  pupils  are  absent,  how 
many  are  present  ? 

18.  What  number  must  be  added  to  9  to  make  52  ?    to 
make  73  ? 

t!9.  A  boy  having  a  kite  string  82  yd.  long  lost  7  yd.  in 
the  telephone  wires.    How  many  yards  had  he  left  ? 

V20.  A  girl  and  her  cat  together  weigh  62  Ib.,  and  the  cat 
weighs  8  Ib.    How  much  does  the  girl  weigh  ? 

21.  For  a  room  and  entrance  hall  33  yd.  of  carpet  are 
required.  For  the  hall  7  yd.  are  needed.  How  much  is 
needed  for  the  room  ? 


INTEGERS 
15.   Minuend  ending  in  4,  5,  or  6 


1. 

34 

-4. 

5. 

54 

-8. 

9. 

75 

-5. 

13. 

26- 

8. 

2. 

24 

—  7. 

6. 

64 

-3. 

10. 

36 

—  7. 

14. 

35- 

8. 

3. 

44 

-9. 

7. 

94 

-2. 

11. 

75 

-9. 

15. 

65- 

6. 

4. 

34 

-5. 

8. 

24 

-6. 

12. 

36 

-9. 

16. 

35- 

7. 

17.  What  number  must  be  added  to  7  to  make  35?  to 
make  84  ? 

.  18.  If  a  dealer  has  54  qt.  of  peanuts  and  sells  9  qt.,  how 
many  quarts  has  he  left  ? 

v  19.  If  I  had  74  crayons  yesterday  and  8  less  to-day,  how 
many  have  I  now  ? 

20.  The  distance  from  here  to  a  certain  place  X  is  65  mi. 
How  far  is  it  to  a  place  6  mi.  this  side  of  X  ? 

21.  There  are  84  pupils  in  a  certain  school  and  5  were 
absent  on  Monday.    How  many  were  present  ? 

16.   Minuend  ending  in  7  or  8,  and  Review 


1.  27  -  8. 
2.  47  -  9. 
3.  38-9.. 
4.  62-8. 

5.  43  -  6. 
6.  75-7. 
7.  60-3. 
8.  41  -  6. 

9.  26  -  9. 
10.  32  —  7. 
11.  23-5. 
12.  85-8. 

13.  68-9. 
14.  77  -  8. 
15.  31  -  7. 
16.  92-6. 

17.  How  much  is  65  yr.  minus  7  yr.  ? 

18.  If  a  dealer  has  91  qt.  of  milk  and  sells  8  qt.,  how 
many  quarts  has  he  left  ? 

19.  If  you  made  a  score  of  53  in  a  game  and  I  made  6 
less,  how  much  did  I  make  ? 

20.  If  a  flag  pole  75  ft.  high  broke  off  7  ft.  from  the  top, 
how  much  remained  standing  ? 

21.  If  an  exercise  has  22  examples  and  you  have  solved 
8,  how  many  are  left  to  be  solved  ? 

22.  If  a  dealer  bought  93  qt.  of  berries  and  7  qt.  were 
spoiled,  how  many  quarts  of  good  berries  had  he? 


SUBTRACTION  9 

17.    Subtraction.    No  Reduction 

Think  of  87  -  25  as  87  -  20  -  5,  or  67  -  5.    State  aloud  only  the 
result,  62. 

1.  86  -  10.  5.  48  -  20.  9.  38  -  27.  13.  98  -  56. 

2.  73  -  10.  6.  67  -  23.  10.  53  -  23.  14.  77  -  44. 

3.  42  -  11.  7.  75  -  32.  11.  87  -  51.  15.  81  -  31. 

4.  75  -  12.  8.  86  -  45.  12.  96  -  32.  16.  68  -  25. 

17.  What  number  must  be  added  to  23  to  make  75? 

18.  If  Mr.  A  has  $75  and  spends  $42,  how  much  is  left? 
v  19.  If  a  girl  has  27  yd.  of  ribbon  and  uses  15  yd.,  how 

many  yards  has  she  left? 

20.  If  a  man  sells  32  acres  from  a  lot  of  96  acres,  how 
many  acres  has  he  left  ? 

21.  Our  flag  has  46  stars  and  13  stripes.    How  many  more 
stars  than  stripes  -are  there  in  our  flag  ? 

18.   Reduction  required 

Think  of  75  -  36  as  75  -  30  -  6,  or  45  -  6.    State  aloud  only  the 
result,  39. 


1. 

75 

-30. 

5. 

86- 

20. 

9. 

54 

-20. 

13. 

31 

-20. 

2. 

75 

-32. 

6. 

86- 

24. 

10. 

54 

-23. 

14. 

31 

-21. 

3. 

75 

-35. 

7. 

86- 

26. 

11. 

54 

-24. 

15. 

31 

-22. 

4. 

75 

-38. 

8. 

86- 

29. 

12. 

54 

-28. 

16. 

31 

-24. 

17.  What  number  subtracted  from  72  leaves  38  ? 

18.  Mr.  B  has  82  cows  and  sells  45.    How  many  are  left? 

19.  A  man  52  yr.  old  is  43  yr.  older  than  his  son.    How 
old  is  his  son  ? 

20.  A  building  is  62  ft.  high   and   the   lowest   story  is 
16aft.  high.    How  high  is  it  above  the  lowest  story? 

v.21.  A  man  went  around  the  world  in  63  days  and  was 
16  days  in  crossing  the  Pacific.  How  long  did  it  take  for 
the  rest  of  the  journey  ? 


10  INTEGERS 

19.  Subtracting  from  100 

Think  of  100  -  67  as  90  -  60  and  10  -  7,  or  33.    It  may  also  be 
thought  of  as  40  —  7. 

1.  100-28.  5.  100-78.  9.  100-77.  13.  100-69. 

2.  100-32.  6.  100-51.  10.  100-30.  14.  100-70. 

3.  100-46.  7.  100-24.  11.  100-45.  15.  100-49. 

4.  100-19.  8.  100-83.  12.  100-78.  16.  100-81. 

17.  I  owe  82/  and  pay  a  dollar.    How  much  change  is 
due?- 

18.  I  owe  48/  and  pay  a  dollar.    How  much  change  is 
due? 

19.  I  owe  17^  and  32  /  and  pay  a  dollar.    How  much 
change  is  due  ? 

20.  My  purchases  at  a  store  amount  to  35/  and  16/. 
How  much  change  is  due  from  $1  ? 

20.  Making  Change  to  $1 

Find  the  change  due  from  $1  if  you  make  purchases  of: 


1.  10/. 

13.  27/. 

25.  78/. 

.  37.  46/. 

49.  60/. 

2.  42X- 

14.  32/. 

26.  43/. 

38.  59/. 

50.  88/. 

3.  71/. 

15.  49/. 

27.  45/. 

39.  6S/. 

51.  56/. 

4.  33/. 

16.  34/. 

28.  50/. 

40.  37/. 

52.  99/. 

5.  24/. 

17.  31  /. 

29.  58/. 

41.  72/. 

53.  65/. 

6.  SIX- 

18.  35/. 

30.  38/. 

42.  47/. 

54.  69/. 

7.  30/. 

19.  39/. 

31.  54/. 

43.  74/. 

55.  83/. 

8.  44/. 

20.  94/. 

32.  61  /. 

44.  77/. 

56.  70/. 

9.  25/. 

21.  52/. 

33.  73/. 

45.  75/. 

57.  93/. 

10.  36/. 

22.  64/. 

34.  89/. 

46.  63/. 

58.  66/. 

11.  26/. 

23.  48/. 

35.  82/. 

47.  92/. 

59.  8V- 

12.  23/. 

24.  87/. 

36.  55/. 

48.  86/. 

60.  79/. 

61.     5X 

+  10/  +  25 

/.           63. 

30/  +  50/  + 

10/. 

62.  25/ 

+  25/  +  15 

X-           64. 

15/  +  35/  + 

45/. 

SUBTRACTION  ^  11 

21.  Subtracting  from  Hundreds 

Think  of  200  -  68  as  190  -  60  and  10  -  8,  or  132.  It  may  also  be 
thought  of  as  140  -  8. 

1.  200-52.  5.  300-33.  9.  500-20.  13.  600-47. 

2.  200-75.  6.  300-74.  10.  600-39.  14.  700-63. 

3.  200-36.  7.  400-67.  11.  700-48.  15.  800-49. 

4.  200-61.  8.  400-88.  12.  800-27.  16.  900-90. 

17.  I  owe  78/.    How  much  change  is  due  from  $2  ? 

18.  If  you  owe  91/,  how  much  change  is  due  from  $2  ? 

19.  If  your  purchases  amount  to  35/  and  IS/,  how  much 
change  is  due  from  $5  ? 

20.  How  much  must  be  added  to  38/  to  make  $6  ?    to 
make  $7  ?    to  make  99/  ? 

21.  What  year  is  63  years  before  1900  ?    What  year  is 
89  years  before  2000  ?    77  years  before  2000  ? 

22.  Subtracting  from  Hundreds 

1.  200-27.  5.  300-62.  9.  400-54.  13.  500-23. 

2.  200-59.  6.  300-78.  10.  400-35.  14.  500-41. 

3.  200-46.  7.  300-49.  11.  400-21.  15.  500-28. 

4.  200-38.  8.  300-^7.  12.  400-39.  16.  500-32. 

17.  If  I  have  $1  and  spend  77/,  how  much  have  I  left  ? 

18.  If  I  have  $2  and  spend  50/,  how  much  have  I  left  ? 

19.  If  I  have  $5  and  spend  78/,  how  much  have  I  left  ? 

20.  If  a  fruit  grower  has  300  trees,  all  but  38  bearing 
fruit,  how  many  are  bearing  ? 

:-21.  If  a  farmer  has  200  acres,  46  being  wooded,  how 
many  acres  are  not  wooded  ? 

*-22.  If  I  owe  50/  and  42/,  how  much  change  should  I 
receive  from  $5  ? 

23.  If  I  owe  75/  and  16/,  how  much  change  should  I 
•receive  from  $2  ? 


12  INTEGERS 

23.  Making  Change 

To  give  the  change  due  from  $5  on  a  purchase  of  $2.45,  a  merchant 
thinks  "5  (to  make  250)  and  250  (to  make  500)  are  255,"  and  he 
pays  $2.55. 

Find  the  change  due  from  $2  if  you  make  purchases  of: 

1.  $1.40.      3.  $1.75.      5.  $1.10.      7.  $1.23.       9.  $1.38. 

2.  $1.72.      4.  $1.48.      6.  $1.66.      8.  $1.78.     10.  $1.17. 

Also  the  change  due  from  $3 : 

11.  $2.24.    12.  $2.06.    13.  $2.55.    14.  $2.65.     15.  $2.03. 

Also  the  change  due  from  $5 : 

16.  $4.32.    17.  $3.75.    18.  $2.60.    19.  $1.45.     20.  $2.05. 
21.  If  your  purchases  amount  to  $1,  $1.25,  and  40/,  how 
much  change  is  due  you  from  $5  ? 

24.  Making  Change 

Fihd  the  change  due  from  $2  if  you  make  purchases  of: 

1.  $1.25.      4.  $1.15.      7.  $1.58.    10.  $1.81.    13.  $0.28. 

2.  $1.50.      5.  $1.27.      8.  $1.72.    11.  $1.07.    14.  $0.41. 

3.  $1.35.      6.  $1.36.      9.  $1.49.    12.  $1.63.    15.  $0.90. 

Also  the  change  due  from  $5 : 

16.  $2.40.  20.  $4.25.  24.  $1.95.  28.  $3.49.  32.  $3.41. 

17.  $3.50.  21.  $3.35.  25.  $2.90.  29.  $2.81.  33.  $1.09. 

18.  $3.75.  22.  $4.65.  26.  $1.26.  30.  $1.77.  34.  $2.07. 

19.  $1.25.  23.  $2.85.  27.  $2.38.  31.  $2.68.  35.  $4.30. 

36.  If  your  purchases  amount  to  15/,  35/,  and  50,/,  what 
is  the  total  ? 

37.  If  your  purchases  amount  to  22 /,  25 /,  and  35/,  and 
you  give  the  dealer  a  dollar  bill,  how  much  change  should 
you  receive  ? 


9. 

3 

x 

7. 

17. 

4 

X 

4. 

25. 

5 

x 

5. 

10. 

3 

X 

5. 

18. 

4 

X 

6. 

26. 

5 

x 

3. 

11. 

3 

X 

8. 

19. 

4 

X 

3. 

27. 

5 

X 

7. 

12. 

3 

X 

6. 

20. 

4 

X 

8. 

28. 

5 

X 

9. 

13. 

3 

X 

3. 

21. 

4 

X 

7. 

29. 

5 

X 

4. 

14. 

3 

X 

9. 

22. 

4 

X 

2. 

30. 

5 

X 

2. 

15. 

3 

X 

2. 

23. 

4 

X 

9. 

31. 

5 

x 

8. 

16. 

3 

X 

4. 

24. 

4 

X 

f 

5. 

32. 

5 

X 

6. 

MULTIPLICATION  13 

25.  Review  of  the  Multiplication  Table 

Following  the  custom  of  most  modern  American  writers,  the  multi- 
plier is  placed  first  in  these  exercises.  Thus,  2  x  15  is  read  "  2  times  15. " 

1.  2  x  3. 

2.  2x7. 

3.  2x4. 

4.  2x6. 

5.  2x9. 

6.  2x2. 

7.  2x8. 

8.  2  x  5. 

33.  2  x  3  x  4  is  how  much  greater  than  2x2x3? 

34.  2  x  4  x  2  is  how  much  greater  than  2x3x2? 

35.  2  x  4  x  5  is  how  much  greater  than  2x4x3? 

36.  3  x  3  x  2  is  how  much  less  than  4x3x2? 

26.  Review  of  the  Multiplication  Table 

1.  6  x  5. 

2.  6x3. 

3.  6x9. 

4.  6x7. 

5.  6x2. 

6.  6x6. 

7.  6x4. 

8.  6x8. 

33.  2  x  2  x  2  is  how  much  less  than  2x3x3? 

34.  By  what  number  must  2x2x3  be  multiplied  to 
be  equal  to  36  ? 

35.  By  what  number  must  3x3x3  be  multiplied  to 
be  equal  to  54? 

36.  By  what  number  must  5x5x2  be  multiplied  to 
be  equal  to  10  x  10  x  2? 


9. 

7 

x 

3. 

17. 

8x 

6., 

25. 

9x 

5. 

10. 

7 

x 

7. 

18. 

8x 

3. 

26. 

9x 

4. 

11. 

7 

X 

9. 

19.  1 

5x 

5. 

27. 

9x 

9. 

12. 

7 

X 

5. 

20.  J 

5x 

9. 

28. 

9x 

7. 

13. 

7 

X 

8. 

21.  : 

Sx 

2. 

29. 

9x 

3. 

14. 

7 

X 

4. 

22.  i 

Sx 

8. 

30. 

9x 

8. 

15. 

7 

X 

2. 

23.  i 

3x 

4. 

31. 

9x 

2. 

16. 

7 

X 

6. 

24.  , 

8x 

7. 

32. 

9x 

G. 

14  INTEGERS 

27.   Review  of  the  Multiplication  Table 


1.  4  x  8. 

12.  8x9. 

23.  2x5. 

34.  9x8. 

2.  5x9. 

13.  5x7. 

24.  9x7. 

35.  3x7. 

3.  5x6. 

14.  7x9. 

25.  9x9. 

36.  9x6. 

4.  4x5. 

15.  5x5. 

26.  9x5. 

37.  7x5. 

5.  4x4. 

16.  8x4. 

27.  8x6. 

38.  8x7. 

6.  6x7. 

17.  6x6. 

28.  6x9. 

39.  6x5. 

7.  7x7. 

18.  2x9. 

29.  7x8. 

40.  8x5. 

8.  3  x  6. 

19.  3x5. 

30.  3x8. 

41.  6x4. 

9.  3x4. 

20.  4x6. 

31.  4x7. 

42.  9x4. 

10.  2x4. 

21.  4x9. 

32.  8x8. 

43.  9x2. 

11.  6x8. 

22.  5x8. 

33.  3x9. 

44.  9x3. 

45. 

2x2x2. 

48.  2x 

2x2x2. 

46. 

2x5x2. 

49.  2x 

2x2x3. 

47. 

5x2x3. 

50.  2x 

2x3x3. 

28.   Two-figure  Multiplicand 

1.  2  x  10.  6.  7  x  20.  11.  3  x  13.  16.  6  x  31. 

2.  3  x  20.  7.  8  x  30.  12.  4  x  21.  17.  7  x  40. 

3.  4  x  20.  8.  9  x  20.  13.  5  x  20.  18.  7  x  41. 

4.  5  x  11.  9.  2  x  12.  14.  5  x  21.  19.  9  x  50. 

5.  6  x  11.  10.  2  x  23.  15.  6  x  30.  20.  9  x  51. 

21.  At  12/  a  yard,  what  will  4  yd.  of  ribbon  cost  ? 

22.  At  13/  a  pound,  what  will  3  Ib.  of  meat  cost  ? 

23.  At  22^  a  dozen,  what  will  4  doz.  peaches  cost  ? 

24.  At  32  /  a  pound,  what  will  3  Ib.  of  butter  cost  ? 

25.  If  one  bushel  of  wheat  costs  92/,  what  will  3  bu.  cost  ? 

26.  At  70/  a  yard,  what  will  2  yd.  of  matting  cost  ? 

27.  At  60  Ib.  to  a  bushel,  how  much  will  7  bu.  of  wheat 
weigh  ? 

28.  At  21  Ib.  to  a  foot,  how  much  will  7  ft.  of  iron  pipe 
weigh  ? 


MULTIPLICATION  15 

29.  Two-figure  Multiplicand 

It  is  easy  to  multiply  27  by  3  mentally.    Think  of  3  x  27  as  3  x  20 
and  3  x  7,  or  60  -f  21  =  81.    State  aloud  only  81. 

1.  2  x  20.         5.  3  x  20.  9.  3  x  30.         13.  3  x  40. 

2.  2  x  22.         6.  3  x  23.         10.  3  x  32.         14.  3  x  41. 

3.  2  x  23.         7.  3  x  25.         11.  3  x  34.         15.  3  x  43. 

4.  2  x  27.         8.  3  x  26.         12.  3  x  35.         16.  3  x  44. 
i!7.  At  28/  a  pound,  what  will  3  Ib.  of  meat  cost  ? 

iJL8.  At  24  /  a  yard,  what  will  4  yd.  of  cloth  cost  ? 

19.  How  many  inches  in  7  ft.  ?    in  8  ft.  ?    in  9  ft.  ? 

20.  If  the  side  of  a  square  is  34  in.,  how  long  is  the 
perimeter  ? 

21.  If  each  side  of  a  triangle  is  25  in.,  how  long  is  the 
perimeter  ? 

22.  At  17  Ib.  each,  how  much  will  8  bicycles  weigh? 

30.  Two-figure  Multiplicand 


1.  4  x  20. 
2.  4  x  21. 
3.  4  x  22. 
4.  4  x  23. 

5.  5x20. 
6.  5x21. 
7.  5  x  22. 
8.  5  x  23. 

9.  6  x  20. 
10.  6  x  21. 
11.  6x22. 
12.  6x23. 

13.  7x31. 
14.  8  x  30. 
15.  8  x  32. 
16.  9  x  12. 

17.  How  much  is  2  x  12  and  3  x  12  ? 

18.  How  much  is  2  x  15  and  4  x  15  ? 

19.  At  $45  a  head,  how  much  are  5  head  of  cattle  worth  ? 

20.  If  each  side  of  a  triangle  is  27  in.  long,  how  long  is 
the  perimeter  ? 

k21.  If  each  side  of  a  six-sided  flower  bed  is  13  ft.  long, 
how  long  is  the  perimeter  ? 

22.  If  each  can  of  fruit  weighs  3  Ib.,  how  much  will  36 
cans  of  fruit  weigh  ? 

23.  At  $48  each,  how  much  will  6  sets  of  bedroom  fur- 
niture cost? 


16  INTEGERS 

31.  Two-figure  Multiplicand 

1.6x30.          3.6x32.          5.9x10.  7.9x20. 

2.  6  x  31.          4.  7  x  32.          6.  9  x  13.          8.  9  x  22. 
9.  At  60/  a  yard,  how  much  will  6  yd.  of  cloth  cost  ? 

10.  At  65/  a  dozen,  how  much  will  2  doz.  pencils  cost  ? 

11.  At  32/  each,  how  much  will  4  baseball  bats  cost? 

12.  At  65/  a  dozen,  how  much  will  3  doz.  tablets  cost  ? 

13.  At  23/  a  dozen,  how  much  will  5  doz.  bananas  cost  ? 

14.  At  70/  a  yard,  how  much  will  8  yd.  of  carpet  cost  ? 

15.  At  $42  a  head,  how  much  will  5  head  of  cattle  cost  ? 

16.  At  $32  each,  how  much  will  6  bicycles  cost  ? 

17.  At  $3  each,  how  much  will  12  school  desks  cost  ? 

18.  At  $7  each,  how  much  will  22  sheep  cost  ?  32  sheep  ? 

19.  At  12/  a  pair,  how  much  will  7  pairs  of  silk  shoe 
laces  cost  ?    5  pairs  ?    9  pairs  ? 

32.  Two-figure  Multiplicand 


1.  3  x  22. 
2.  3x27. 
3.  3  x  36. 
4.  4  x  35. 

5.  5x30. 
6.  5x32. 
7.  5  x  34. 
8.  5  x  35. 

9.  7  x  21. 
10.  7x22. 
11.  8x21. 
12.  8  x  22. 

13.  9  x  40. 
14.  9x41. 
15.  9  x  42. 
16.  9  x  45. 

17.  I  bought  3  lamps  at  $2  each.    How  much  change 
should  I  receive  from  $10  ? 

18.  I  bought  12  chairs  at  $3  each.    How  much  change 
should  I  receive  from  $50  ? 

V  19.  I  bought  5  yd.  of  cloth  at  40/  a  yard.  How  much 
change  should  I  receive  from  $5  ? 

\/20.  I  bought  12  yd.  of  cloth  at  8/  a  yard.  How  much 
change  should  I  receive  from  $1  ? 

^21.  A  farmer  bought  a  cow  for  $40,  2  sheep  at  $6  each, 
and  a  harness  for  $30.  How  much  did  he  pay  for  all  ? 
What  change  should  he  receive  from  $100  ? 


MULTIPLICATION  it 

33.  Cost  of  Purchases 

Find  the  cost  of  the  following : 

1.  6  books  at  SI/.  13.  8  yd.  of  carpet  at  70/. 

2.  3  Ib.  of  tea  at  42/.  14.  5  cans  of  cocoa  at  41/. 

3.  4  cows  at  $41.  15.  9  gal.  of  gasoline  at  21/. 

4.  6  Ib.  of  steak  at  21/.  16.  7  tennis  balls  at  20/. 

5.  7  collars  at  21/.  17.  3  writing  tablets  at  15/. 

6.  7  Ib.  of  butter  at  30/.  18.  6  flags  at  15/. 

7.  6  Ib.  of  figs  at  15/.  19.  12  pencils  at  3/. 

8.  2  bu.  of  wheat  at  90/.  20.  15  trout  flies  at  8/. 

9.  9  Ib.  of  meat  at  20/.  21.  21  yd.  of  ribbon  at  9/. 

10.  8  Ib.  of  walnuts  at  15/.     22.  12  Ib.  of  sugar  at  6/. 

11.  3  Ib.  of  cheese  at32/.      23.  18  doz.  buttons  at  5/. 

12.  9  cans  of  soup  at  12/.      24.  4  sewing  machines  at  $42. 

34.  Cost  of  Purchases 

Find  the  cost  of  the  following,  and  the  change  due  from 
the  amount  paid : 

1.  8  books  at  30/.   Paid  $5. 

2.  5  Ib.  'of  tea  at  60/.    Paid  $5. 

3.  6  cans  of  peas  at  15/.    Paid  $1. 

4.  6  Ib.  of  roast  beef  at  20/.   Paid  $1.25. 

5.  5  yd.  of  cloth  at  90/.    Paid  $5. 
w-6.  7  writing  tablets  at  12/.   Paid  $1. 

7.  2  pencils  at  5/  and  3  tablets  at  12/.    Paid  50/. 

1^8.  3  cows  at  $40  and  2  sheep  at  $6.    Paid  $140. 

9.  2  horses  at  $125  and  a  carriage  at  $100.   Paid  $400. 

10.  5  acres  of  land  at  $90  and  2  acres  at  $50.    Paid  $600. 

^11.  7  cows  at  $50  and  6  cows  at  $40.    Paid  $600. 

12.  5  tables  at  $15  and  20  desks  at  $4.    Paid  $160. 

;    13.  8  chairs  at  $2  and  a  table  at  $9.    Paid  $30. 


18  INTEGERS 

35.   Cost  of  Purchases 

Find  the  cost,  and  the  change  due  from  the  amount  paid : 

1.  2  cows  at  $46.   Paid  $100. 

2.  3  Ib.  of  coffee  at  35/.    Paid  $1.10. 

3.  4  yd.  of  cloth  at  27/.    Paid  $1.25. 

4.  5  kitchen  stoves  at  $33.   Paid  $165. 

5.  6  cans  of  peaches  at  17/.    Paid  $1.10. 

6.  7  gold  watches  at  $44.    Paid  $308. 

7.  8  Ib.  of  meat  at  18/.    Paid  $1.50. 

8.  9  yd.  of  silk  at  45/.    Paid  $4.25. 

9.  24  Ib.  sugar  at  6/.   Paid  $1.50. 

10.  48  postage  stamps  at  2/.    Paid  $1. 

11.  75  street-car  tickets  at  5/.    Paid  $5. 

12.  36  bottles  of  mucilage  at  5/.   Paid  $2. 

13.  4  doz.  hats  at  $2  apiece.   Paid  $100. 

36.   Measures 

1.  3  x  23  in.  7.  5  x  14  ft.  13.  15  x  3  yd. 

2.  3  x  27  in.  8.  5  x  28  ft.  14.  24  x  2  rd. 

3.  3  x  36  in.  9.  5  x  32  ft.  15.  35  x  4  rd. 

4.  4  x  25  in.  10.  6  x  12  rd.  16.  21  x  5  sq.  ft. 

5.  4  x  27  in.  11.  6  x  14  rd.  17.  23  x  4  sq.  in. 

6.  4  x  36  in.  12.  6  x  18  rd.  18.  33  x  5  sq.  yd. 

19.  If  one  side  of  a  square  is  27  in.,  what  is  the  perimeter? 

20.  If  one  side  of  a  square  is  46  in.,  what  is  the  perimeter  ? 

21.  If  each  side  of  a  triangle  is  36  in.,  what  is  the 
perimeter  ? 

22.  If  a  schoolroom  is  32  ft.  long  and  22  ft.  wide,  what 
is  the  perimeter  ? 

23.  If  you  have  made  a  kite  with  four  sides,  two  being 
18  in.  each,  and  the  other  two  24  in.  each,  what  is  the 
perimeter  of  the  kite  ? 


DIVISION  19 

37.   Dividing  by  2 


1.  20  -=-2. 
2.  40  -«-  2. 
3.  60  -r-  2. 
4.  80-2. 

5.  22  -  2. 
6.  44-5-2. 

7.  66-2. 
8.  88  -s-  2. 

9.  24-5-2. 
10.  46-5-2. 
11.  62-5-2. 

12.  84  -5-  2. 

13.  28  -=-2. 
14.  42-5-2. 
15.  68-5-2. 
16.  86-5-2. 

17.  At  2/  each,  how  many  postage  stamps  can  you  buy 
for82/? 

18.  At  2/  each,  how  many  newspapers    can  you  buy 
for  48/? 

19.  At  2  ft.  to  a  step,  how  many  steps  would  you  take  in 
walking  64  ft.  ? 

20.  At   2/   a   mile,   how   many   miles    can   you    travel 
for  $1.80? 

21.  How  many  quarts  are  there  in  2  pt.  ?   in  26  pt.  ?    in 
48  pt.?    in  64  pt.?    in  82  pt.? 

38.   Dividing  by  2  or  3 


1.  30-2. 
2.  50-4-2. 
3.  70-5-2. 
4.  90-^2. 

5.  36-2. 
6.  54-2. 
7.  72-2. 
8.  92  -  2. 

9.  30  -  3. 
10.  60-3. 
11.  90-5-3. 
12.  33-3. 

13.  96-3. 
14.  24-3. 
15.  45  -  3. 
16.  54-3. 

17.  At  2^  each,  how  many  pencils  can  you  buy  for  38/? 

18.  At  3X  each,  how  many  pencils  can  you  buy  for  42/? 

19.  At  3/  each,  how  many  erasers  can  you  buy  for  45/  ? 

20.  At   2/  each,   how   many   penholders    can  you  buy 
for  52X? 

21.  At  3/  a  yard,  how  many  yards  of  ribbon  can  you 
buy  for  78/? 

22.  At   3/  each,  how  many  newspapers  can  you  buy 
for  48/? 

23.  If  one  pair  of  shoes  cost  $3,  how  many  pairs  can  be 
bought  for  $51? 


20  INTEGERS 

39.   Dividing  by  4,  5,  or  6 

To  divide  62  by  4,  think  of  dividing  40  +  12  by  4.    Think  of  the 
sum  of  10  +  3,  but  state  only  the  result,  13. 


1.    44  -  4. 

2.  48  -r-  4. 
3.  52-:-  4. 
4.  64  -=-4. 

5.  72-4. 
6.  88  -=-4. 
7.  92-4. 
8.  96  -=-4. 

9.  65-5. 
10.  70-5. 
11.  85  -  5. 
12.  90-5. 

13.  72-6. 
14.  84-6. 
15.  90  —  6. 
16.  96  —  6. 

17.  At  4/  each,  how  many  cakes  can  be  bought  for  68/  ? 

18.  At  5/  each,  how  many  pads  can  be  bought  for  75/  ? 

19.  At  6/  each,  how  many  erasers  can  be  bought  for  78/? 

20.  At  $6  each,  how  many  sheep  can  be  bought  for  $102? 

21.  At  5/  each,  how  many  trolley  tickets  can  be  bought 
for  95/  ? 

22.  How  many  4-cent   postage   stamps   can  be  bought 
for  76/  ? 

40.   Dividing  by  7,  8,  or  9 

To  divide  128  by  8,  think  of  dividing  80  +  48  by  8.    State,  however, 
only  the  result,  16. 


1. 

77 

-7. 

5. 

96-8. 

9. 

99  -j-  9. 

13. 

270 

-9. 

2. 

84 

-7. 

6. 

160  -*-  8. 

10. 

108 

— 

9. 

14. 

360 

-9. 

3. 

91 

-7. 

7. 

168  -f-  8. 

11. 

117 

— 

9. 

15. 

450 

-9. 

4. 

88 

^-8. 

8. 

240  -  8. 

12. 

126 

-i- 

9. 

16. 

540 

-9. 

17.  At  $7  each,  how  many  tables  can  be  bought  for  $140  ? 

18.  At  $7  each,  how  many  rugs  can  be  bought  for  $147  ? 

19.  At  7/  each,  how  many  rulers  can  be  bought  for  84/  ? 

20.  At  8/  a  yard,  how  much  cloth  can  be  bought  for  96/? 
V21.  At  $8  each,  how  many  chairs  can  be  bought  for  $72  ? 

22.  How  many  9's  are  there  in  270  ?    in  279  ?   in  288  ? 

23.  At  $9  each,  how  many  trunks  can  be  bought  for  $198  ? 

24.  At  9^  each,  how  many  cans  of  soup  can  be  bought 
for  18^  ?   for  $1.80  ? 


DIVISION  21 

41.  Division  with  Remainder 

In  dividing  21  by  2  we  may  proceed  as  follows :    21  -r-  2  =  10,  and 
1  remainder. 

1.5-^2.  5.  8  --3.  9.9-4.  13.  26  -=-  5. 

2.  21  -r-  2.  6.  32  -=-  3.  10.  45  -=-  4.  14.  37  -*-  5. 

3.  45  -*-  2.  7.  61  -=-  3.  11.  47  H-  4.  15.  48  -=-  5. 

4.  51  -H  2.  8.  28  -5-  3.  12.  66  -^  4.  16.  54  --  5. 

17.  What  is  the  remainder  when  38  is  divided  by  6  ? 

18.  How  do  the  remainders  of  54  -4-  7  and  68  -H  7  compare  ? 

19.  How  much  larger  is  the  remainder  of  72  -j-  7  than 
that  of  65  -s-  8  ? 

/x20.  What  number  can  you  add  to  38  so  that  the  result 
divided  by  5  shall  have  no  remainder  ? 

f/2l.  What  number  can  you  subtract  from  38  so  that  the 
result  divided  by  5  shall  have  no  remainder  ? 

42.  Division  with  Remainder 


1.  37  -s-  6. 

2.  44  -*•  6. 

3.  33  -5-  6. 
4.  53  -s-  6. 

5.  37-5-7. 
6.  45-5-7. 
7.  69-5-7. 

8.  74-*-  7. 

9.  27  -*-  8. 
10.  37-*-  8. 
11.  63-5-8. 
12.  67-5-8. 

13.  28-*-  9. 
14.  38-5-9. 
15.  50  •*•  9. 
16.  80-5-9. 

17.  At  $4  a  dozen,  how  many  dozen  cans  of  peaches  can 
be  bought  for  $70,  and  how  much  money  will  be  left  ? 

18.  A  man  buys  as  many  bridles  as  possible  for  $100, 
paying  $9  apiece.    How  many  does  he  buy  and  how  much 
money  has  he  left  ? 

19.  What  is  the  remainder  when  10  is  divided  by  9  ? 
when  20  is  divided  by  9  ?    30  ?  40  ?  50  ?   60  ?  70  ?  80  ? 

20.  What  are  the  remainders  when  12  and  1  +  2  are 
divided  by  9  ?  when  23  and  2  +  3  are  divided  by  9  ?  also 
35  and  3  +  5  ?   also  41  and  4  +  1  ?    also  52  and  5  +  2  ? 
also  62  and  6  +  2  ?   Do  you  see  some  law  in  all  these  ? 


22  INTEGERS 

43.   Division  with  Remainder 


1.  41  -  2. 
2.  53  --2. 
3.  37-3. 
4.  55  -=-3. 

5.  82-4-4. 
6.  75-4. 
7.  52-5-5. 
8.  63  -  5. 

9.  38 
10.  56 

11.  75 
12.  85 

-=-6. 
•*-6. 

-s-  7. 

rr 

13.  83-*-  8. 
14.  SO-i-8. 
15.  97-9. 
16.  75-5-9. 

17.  What  is  the  remainder  when  771  is  divided  by  7  ? 

18.  What  are  the  remainders  of  442  —  4  and  302  —  3  ? 

19.  What  is  the  smallest  number  that  you,  can  add  to  72 
so  that  when  you  divide  by  5  there  shall  be  no  remainder  ? 

20.  What  is  the  smallest  number  that  you  can  add  to  75 
so  that  when  you  divide  by  9  there  shall  be  no  remainder  ? 

21.  At  $6  each,  how  many  school  desks  can  be  bought 
for  $100,  and  how  much  will  be  left  over  ? 

22.  What  number  can  you  subtract  from  89  so  that  when 
you  divide  by  7  there  shall  be  no  remainder  ? 

44.   Fraction  in  the  Quotient 

Instead  of  stating  a  remainder  it  is  customary  to  express  a  fraction 
in  the  quotient,  thus  :    37  4-  5  =  7f .    Similarly,  66  -=-  8  =  8|,  or  8J. 


1.  23-2. 
2.  34-3. 
3.  33-4. 
4.  44-5. 

5.  44-6. 
6.  72-7. 
7.  68-8. 
8.  93-9. 

9.  39  -  6. 
10.  55-6. 

11.     71-;-  7. 

12.  93-7. 

13.  39-8. 
14.  51-5-8. 
15.  71  -r-  9. 
16.  93-9. 

17.  How  much  is  \  of  101  ?    How  much  is  \  of  202  ? 

18.  If  $441  is  divided  equally  among  4  people,  what  is 
the  share  of  each  ? 

19.  If  the  perimeter  of  a  square  is  27  in.,  what  is  the 
length  of  each  side  ? 

20.  A  figure  bounded  by  5  equal  sides  has  a  perimeter  of 
81  in. '  What  is  the  length  of  each  side  ? 

21.  How  many  square  yards  are  there  in  105  sq.  ft.  ?  in 
452  sq.  ft.  ?   in  723  sq.  ft.  ? 


DIVISION  23 

45.   Fraction  in  the  Quotient 


1. 

43- 

2. 

5. 

40-3. 

9. 

43-4. 

13. 

36 

-5-5. 

2. 

47-5- 

2. 

6. 

20-3. 

10. 

35-=- 

-4. 

14. 

27 

-5-5. 

3. 

49- 

2. 

7. 

26-3. 

11. 

23-5- 

-4. 

15. 

33 

-5. 

4. 

31-5- 

2. 

8. 

29-3. 

12. 

49-4. 

16. 

49 

-5. 

17. 

How 

much 

is 

jQf 

$17? 

fcof 

$23 

9 

18. 

How 

much 

is 

1    Of 

17  in.? 

i  of  25 

in.? 

19.  How  much  is  \  of  15  hr.  ?    J  of  17  hr.  ? 

20.  How  much  is  |  of  20  oz.?    £  of  25  oz.? 

21.  The  perimeter  of  a  square  is  97  in.    What  is  the 
length  of  each  side  ? 

22.  The  perimeter  of  a  triangle  is  28  in.,  and  all  the  sides 
are  equal.    What  is  the  length  of  each  side  ? 

23.  If  47  yd.  of  carpet  is  cut  into  5  equal  strips,  what  is 
the  length  of  each  strip  ? 

46.   Fraction  in  the  Quotient 


1.  35-=-  2. 
2.  55  -  2. 
3.  71  H-  3. 

4.  91  -  3. 

5.  37  -=-4. 
6.  53  -  4. 

7.  71  -5. 

8.  92  H-  5. 

9.  304  H-  3. 
10.  334--  3. 
11.  504  --5. 
12.  554-5. 

13.  704  H-  7. 
14.  773-7. 
15.  903  H-  9. 
16.  996  —  9. 

17.  How  much  is  £  of  $41  ?    £  of  $53  ? 

18.  How  much  is  1  of  $31  ?    £  of  $47  ? 

19.  How  much  is  |  of  27  yd.  ?    \  of  51  yd.  ? 

L&O.  A  flower  bed  having  6  equal  sides  has  a  perimeter  of 
19  ft.    What  is  the  length  of  each  side  ? 

21.  If  4  boys  pick  35  qt.  of  berries  and  divide  them 
equally,  what  is  the  share  of  each  ? 

22.  If  $75  is  divided  equally  among  6  men,  what  is  the 
share  of  each  man  ? 

23.  If  a  man  pays  $884  for  8  horses,  what  is  the  average 
price  per  horse  ? 


24  INTEGERS 

47.   Division  by  Multiples  of  10 

In  dividing  by  a  multiple  of  10,  first  divide  by  10  and  then  by  the 
number  of  tens.    Think  of  560  -H  70  as  56  -r-  7,  and  state  the  result,  8. 

1.  300  -=-30.  5.  660  -=-60.  9.  560 -=- 80. 

2.  630  -=-30.  6.  780 -=-60.  10.  960 -=-80. 

3.  320  -=-40.  7.  630 -=-70.  11.  990 --90. 

4.  750H-50.  8.  840  -=-70.  12.  1080 -- 90. 

13.  How  many  hours  in  720  minutes  ? 

14.  What  is  the  quotient  of  3330  -=-  30  ?    of  6060  --30  ? 

15.  If  we  should  allow  30  days  to  the  month,  how  many 
months  should  we  find  in  1230  days  ? 

16.  How   many  rods   in    1  mi.  ?     How   many  times    is 
20  rd.  contained  in  1  mi.  ? 

17.  At  $50  each,  how  many  cows  can  be  bought  for  $150? 
for  $350  ? 

48.   Review 


1. 

23  +  17. 

5. 

75- 

25. 

9. 

2 

X 

32. 

13. 

91 

-=-7. 

2. 

36  +  25. 

6. 

72- 

26. 

10. 

3 

X 

33. 

14. 

91 

-=-8. 

3. 

48  +  34. 

7. 

83- 

14. 

11. 

4 

X 

53. 

15. 

78 

-=-9. 

4. 

53  +  47. 

8. 

92- 

25. 

12. 

6 

X 

31. 

16. 

75 

H-10. 

17.  How  many  minutes  in  960  sec.  ? 

18.  How  many  yards  in  39  ft.  ?    in  72  ft.  ? 

19.  How  many  pounds  in  16  oz.  ?    in  32  oz.  ?   in  64  oz.  ? 

20.  How  many  horses  at  $90  each  can  be  bought  for 
$1170? 

21.  How  many  library  desks  at  $20  each  can  be  bought 
for  $240  ?    for  $620  ? 

22.  At  $20  each,  how  much  will  10  library  desks  cost  ? 
How  much  will  12  cost  ? 

23.  A  man  buys  goods  for  $435  and  pays  $500.    How 
much  change  is  due  him  ? 


REDUCTION  25 

II.    COMMON  FRACTIONS 
49.   To  Different  Denominators 
Reduce  as  indicated: 

To  lowest  terms  :    1.  f .  2.   |.  3.  f .  4.  f . 

To  fourths  :  5.  J.  6.  f .  7.  T%.  8.  jf . 

To  thirds:  9.  f.          10.  J^_      ir.  f,...          12.  |£. 

To  eighths:  13.  f          14.  f:          15.  J.  16.  \%. 

To  twelfths:         17.  J.          18.  J.          19.  |.  20.  £. 

To  tenths:  21.  £.          22.  $.         23.  f.  24.  /„. 

To  sixths :  25.  £.         26.  1.         27.  §.  28.  TV 

29.  |  ft.  =  how  many  12ths  of  a  foot  ?  how  many  inches  ? 

30.  §  yd.  =  how  many  SGthsof  a  yard?  how  many  inches  ? 

31.  f  of  a  dime  =  how  many  lOths  of  a  dime  ?   how  many 
cents  ? 

50.   Integers  to  Fractions 

5  3x5 

Since  1  =  -  i  therefore  3  = 


To  halves  :         1.  1.  2.  3.  3.  7.  4.  9. 

To  thirds :          5.  2.  6.  4.  7.  5.  8.  7. 

To  fourths :        9.  4.  10.  3.  11.  2.  12.  6. 

To  fifths:          13.  3.  14.  5.  15.  9.  16.  7. 

To  sixths  :        17.  2.  18.  7.  19.  8.  20.  12. 

To  eighths  :     21.  5.  22.  3.  23.  2.  24.  12. 

To  tenths:        25.  6.  26.  7.  27.  3.  28.  15. 

To  twelfths :    29.  4.  30.  2.  31.  3.  32.  12. 

33.  How  many  12ths  of  a  foot  in  a  foot  ? 

34.  How  many  inches  in  a  foot  ?    in  3  ft.  ? 

35.  How  many  lOths  of  a  dime  in  7  dimes  ? 

36.  How  many  cents  in  a  dime  ?    in  9  dimes  ? 


26  COMMOX  FRACTIONS 

51.   Improper  Fractions  to  Integers 

In  reducing  f  to  an  integer,  remember  that  |  means  8-^2,  which 
equals  4.    State  only  the  result,  4. 

Reduce  to  integers : 


1.  f. 

5.  3. 

9.     L2. 

13.  |. 

17.  Y. 

2.  f  . 

6.  §. 

10.  f. 

14.  V- 

18.  y. 

3.  V. 

7.  V- 

11.  -V5. 

15.  ¥'• 

19.  -V. 

4.  V- 

8.  V- 

12.  -Y-- 

16.  -Y-- 

20.  -V-. 

21.  How  many  inches  are  there  in  72  eighths  of  an  inch  ? 

22.  A  boy  has  10  half  dollars.    How  many  dollars  has  he  ? 

23.  Another   boy  has   16   quarters.    How  many  dollars 
has  he  ? 

24.  How  many  hours  are   12  thirds   of   an   hour  ?    12 
fourths  of  an  hour  ? 

52.   Improper  Fractions  to  Mixed  Numbers 

The  improper  fraction  -^  means  14  -4-  4,  which  equals  3|,  and  this 
equals  %\. 

Reduce  to  mixed  numbers  : 


1.  f. 

5. 

1- 

9. 

y- 

13. 

-V- 

17. 

¥• 

2.  J. 

6. 

I- 

10. 

J¥9-- 

14. 

Jg8-- 

18. 

¥• 

3.  ¥• 

7. 

Y- 

11. 

V- 

15. 

¥• 

19. 

V- 

4.  V- 

8. 

¥• 

12. 

¥• 

16. 

¥• 

20. 

-v- 

21.  The  sum  of  §  and  §  and  §  is  §.    Express  this  as  a 
whole  number. 

22.  The  sum  of  §  and  §  is  $.    Express  this  as  a  whole 
number  plus  a  fraction. 

23.  Express  -*£  as  a  whole  number  plus  eighths;  as  a 
whole  number  plus  some  other  fraction. 

24.  If  we  lay  side  by  side  35  strips  of  paper,  each  ^  in. 
wide,  what  will  be  the  total  width  ? 


REDUCTION  27 

53.   Mixed  Numbers  to  Improper  Fractions 

To  reduce  5f  to  an  improper  fraction,  think  of  it  as  -^  +  $,  or  *£. 
State  only  the  result,  -1/  . 

Reduce  to  improper  fractions  : 


1. 

2. 

£ 

6. 

7. 

3f. 

11.  1|. 
12.  1TV 

16.  1TV 

17.  1TV 

21. 
22. 

HI 

3. 

if. 

8. 

2i- 

13.  1TV 

18.  2TV- 

23. 

40^. 

4. 

2i- 

9. 

2f. 

14.  2TV 

19.  2T3?. 

24. 

20i. 

5.  2§.         10.  If         15.  2TV         20.  2T%.         25.  10|. 

26.  Express  6^  as  halves. 

27.  Express  6§  as  thirds.    In  6§  in.  how  many  thirds  of 
an  inch  ? 

28.  Express  4f   as  sevenths.    In  4|  weeks  how  many 
sevenths  of  a  week?    how  many  days? 

54.   Improper  Fractions  Reduced 
Reduce  to  integers  : 

1.  f.  4.  V-  7.  V-  10-  *l-  13.  f|. 

2.  |.  5.  i?2-.  8.  V--  11-  fl-  14-  ^) 

3.  f.  6.  V-  9-  ¥-  12.  H.  15.  ||. 

Reduce  to  mixed  numbers  : 

16.  |.  19.   %°-.  22.  V-.  25.  V--  28-  fi- 

17.  f.  20.  -\3.  23.  ^s3-.  26.  -e/-  29-  ii- 

18.  -y.  21.  -33°-.  24.   V--  27-  If  30-  §§• 

Reduce  to  integers  or  mixed  numbers  : 

31.  */.  34.  f|.  37.  /^.  40.  J-ffi-.         43.   ||. 

32.  ?/.  35-^-  38-  ¥•  41-  ft-  44-  M- 

33.  fj.  36.  W\        39.   9^.  42.  ff  45.  §f. 

46.  Express  -\4^  a&_slxths  ;  as  fourths  ;  as  thirds  ;  as  an 
integer. 


28  COMMON  FRACTIONS 

55.   Reduction  to  Lowest  Terms 

To  reduce  f  £  to  lowest  terms,  mentally  cancel  the  highest  factor 
you  see,  and  continue  until  there  are  no  common  factors. 

Reduce  to  lowest  terms :  . 

1.  TV  6.  fa  11.  fa  16.  fa  21.  fa 

2.  T\.  7.  T%.  12.  /?.  17.  fa  22.  ?e?. 

3.  T\.  8.  T%.  13.  fa  18.  sV  23.  fa 

49  Q      10  14.      10  1Q      12  OA        9 

.     "j^r-  v.     T£.  A*,     ^j.  *w«     32*  »*•    ^f^« 

5-  if.  10.  if.  15.  if.  20.  J|.  25.  if. 

26.  In  measuring  the  thickness  of  some  glass  I  find  that 
it  is  -fa  in.    Express  this  in  lowest  terms. 

27.  A  mechanic  has  a  ruler  marked  in  16ths  of  an  inch. 
In  measuring  a  steel  rod  for  a  machine  he  finds  the  diam- 
eter to  be  if  in.    Express  this  in  lowest  terms. 

56.   Least  Common  Denominator 

Reduce  to  fractions  having  the  least  common  denominator  : 
I-  i>  i-  6.   i,  fa  11.  f,  |.  16.  §,  \. 

311  Oil  1  Q       1       1  1B21 

•    i>  lY  8'    3>  3V  i<J.    $•>  £•  1O-    3>  £• 

4-  i,  TV-  9.  ^  f .  14.  ^  f .  19.  f,  f . 

5.  i,  1.  10.  |,  i.  15.  ^  I  20.  i,  £. 

21.  If  I  wish  to  add  £  and  ^  what  denominator  should 
I  use  for  the  fraction  ?    Express  each  with  that  denominator. 
What  other  denominator  might  I  use  ? 

22.  If  I   wish  to  subtract  J  from  |,  what  denominator 
should  I  iise   for  the  fraction  ?    Express  each  with  that 
denominator. 

23.  Could  I  add  the  fractions  \  and  \,  using  32  as  a  com- 
mon denominator  ?   or  using  16  ?    Is  there  a  better  common 
denominator,  and  if  so  why  is  it  better  ? 


lows  : 

1  +  f  =  Jl 

P  =  i  =  U- 

1. 

7  +  4- 

6.  i-| 

-f- 

11.  - 

t  +  f 

2. 

i  +  i- 

»..H 

-f 

12.  , 

t  +  f 

3. 

i  +  l- 

8.  H 

-f 

13. 

!  +  *• 

4. 

t+i 

9-  H 

-f- 

14.  , 

J  +  t- 

5. 

*+•§• 

10.  n 

-1- 

15. 

i  +  t- 

ADDITION  29 

57.   Addition.    Same  Denominators 

In  adding  fractions  having  the  same  denominator,  proceed  as  fol- 

16.  i  +  f 
17-  |  +  |. 
X8.  f  +  f . 

19.  |  +  f . 

20.  f  +  i- 
^21.  How  much  is  J  yd.  and  f  yd.  ? 

--22.  How  much  is  f  mi.  and  f  mi.  ?    f  mi.  and  |  mi.  ? 

V23.  How  much  is  $£  and  $£  ?   $£  and  $|  ? 
MJ4.  If  I  live  I  mi.  from  the  school  and  you  live  |  mi.  far- 
ther, how  far  from  the  school  do  you  live? 

"25.  A  |-inch  frame  has  a  f-inch  beading  added  to  its 
width.    How  wide  does  this  make  the  frame  ? 

58.   Different  Denominators 

In  adding  fractions  having  different  denominators,  proceed  as  fol- 
lows :  £  +  £  =  £  +  |  =  f .    Also  |+|  =  f  +  f  =  |  =  li. 

If)         I        1  C          4         i        ''  ChOII  1O1I7 

•  f  +  i-  5.   |  +  |.  &  f  +  f-  13.  i  +•  f . 

2.  \  +  \.  6.   i  +  |.  10.   i  +  f  14.  |  +  ^ 

8.   f  +  i-  7.   i  +  |.  11.  i  +  |.  15.  |  +  |. 

4-   i  +  i  8.   ^  +  \.  12.  i  +  f.  16.  |  +  |. 

17.  How  much  is  \  +•  ^  4-  \  ? 

18.  Add  ^  in.,  ^  in.,  and  ^  in.    Add  £  in.  and  |  in. 

19.  How  much  must  be  added  to  1  in.  to  equal  ^  in.  + 1  in.  ? 
i£0.  Two  strips  of  paper,  each  £  in.  wide,  are  placed  side 

by  side.    How  wide  are  the  two  together  ? 

21.  Three  strips  of  ribbon,  each  f  in.  wide,  are  placed  side 
by  side.    How  wide  are  the  three  together  ? 
w-"22.  Four  boards,  each   £   in.   thick,  are  placed  one  on 
another.    How  high  is  the  pile  ? 


30  COMMON  FRACTIONS 

59.  Addition.   Mixed  Numbers 

1.  1£  +  f  5.  2i  +  If.  9.  2\  +  If  13.  3f  +  If 

2.  1\  +  If  6.  2£  +  If  10.  3£  +  2f  14.  3|  -f  2|. 

3.  3£  +  5f  7.  2|  +  2f  11.  2|  +  2|.  15.  2j  -f  2f . 

4.  4£  +  |.  8.  3j  +  lf.  12.  2f  +  lf.  16.  3$  +  If 

17.  How  much  is  $2f  and  $3|  ? 

18.  How  much  is  3^  in.  and  5|  in.? 

19.  How  much  is  5|  in.  and  3|  in.? 

20.  How  much  is  2|  in.  and  5|  in? 

21.  The  three  sides  of  a  triangle  are  2i  in.,  2^  in.,  and 
2f  in.    What  is  the  perimeter  ? 

22.  The  three  sides  of  a  triangle  are  3|  in.,  3|  in.,  and 
3|  in.    What  is  the  perimeter  ? 

23.  The  four  sides  of  a  figure  are  2^  in.,  3^  in.,  3  in.,  and 
3^  in.    What  is  the  perimeter  ? 

60.  Addition.    Mixed  Numbers 

To  add  2|  to  3f  mentally,  first  add  2  and  3|  and  then  add  f, 
thinking  "5|  and  |  are  5y,  or  6|."    State  only  the  answer. 

1.  1^  +  f         5.   1J  +  f  9.   2J  +  f .  13.   21  +  f 

2.  2£  +  If      6.  2^  +  If      10.  3^  +  If-  14.  5^  +  If 

3.  2£  +  i-        7.  3J  +  f.        11.  3£  +  f  15.  4i  +  f. 

4.  3£  +  If.      8.  3£  +  1|.      12.  3£  +  2|.  16.  4f  +  1|. 
17.  How  much  is  2f  in.  and  |  in.? 


18.  How  much  is  $2J,  $2|,  and 

19.  A  lady  decides  to  add  ^  in.  to  the  width  of  a  3f- 
inch  ruffle.    How  wide  will  this  make  itV 

20.  A  picture  frame  incloses  a  space  10|  in.  wide.    Each 
side  of  the  frame  is  2^  in.  wide.    What  is  the  total  width  ? 

21.  Some  writing  paper  is  ruled  \  in.  between  the  lines, 
and  another  kind  is  ruled  \  in.  wider.    What  is  the  distance 
between  the  lines  of  this  second  kind  ? 


follows  :    f  —  f 

—  2  —  1 

~~   8  —  ¥• 

i.  i  -  i- 

5. 

2.  i-i- 

6. 

3-   |  -  i 

7. 

4-1-1- 

8. 

SUBTRACTION  31 

61.   Subtraction.    Same  Denominators 

In  subtracting  fractions  having  the  same  denominator,  proceed  as 

f .  9.  $  -  f .  13.   |  -  f . 

4.  10.  |-i.  14.  I  -  f. 

i.  11.   |  -  J.  15.  I  -  i. 

J.  12.  |  -  f  16.  f  -  f . 

17.  If  a  |-inch  board  is  planed  down  \  in.,  what  is  then 
its  thickness  ? 

18.  If  I  have  three  quarters  of  a  dollar  and  spend  a 
quarter  of  a  dollar,  how  much  have  I  left  ? 

19.  If  from  |  yd.  we  take  f  yd.,  how  many  eighths  of 
a  yard  remain  ?  how  many  fourths  ?  how  many  halves  ? 

20.  If  a  man  having  f  mi.  to  travel  has  gone  f  mi.,  how 
much  farther  has  he  to  go  ? 

62.   Different  Denominators 

1.  i  ~  i-  5.   |  -  f .  9.  f  -  i-  13.   I  -  \. 

2.  i  -  i.  6.  \  -  f .  10.  i  -  \.  14.  |  -  f . 

8.1-1-  *•*-!•  "•  I  -I-  15-1-1- 

41    1  87    1  195    1  1fi3    1 

•     ^  S-.  °'     t  2'  i<4'     ?  4-  1D-     4  B- 

17.  How  much  is  $|  -  $^  ?    $£  -  $1  ? 

18.  How  much  is  |  in.  —  ^  in.?    |  in.  —  i  in.  ? 

19.  What  must  be  subtracted  from  |  to  leave  i? 

•*  o 

20.  What  must  be  added  to  |  to  have  the  sum  %  ? 

21.  If  a  |-inch  board  is  planed  down  i  in.,  and  then  a 
veneer  |  in.  thick  is  put  on,  what  is  the  total  thickness  ? 

22.  If  from  a  strip  of  carpet  |  yd.  wide  a  strip  £  in. 
wide  is  cut,  how  wide  is  the  remainder  ? 

23.  If  to  a  piece  of  cloth  |  yd.  wide  a  ruffle  ^  yd.  is 
added  to  one  side  and  a  width  of  \  yd.  is  cut  from  the 
other  side,  how  wide  is  the  piece  then  ? 


32  COMMON  FRACTIONS 

63.   Integers  minus  Fractions 

Since  2  =  1|,  therefore  2  —  \  =  If.    Proceed  in  the  same  way  for 
any  integer  minus  a  fraction. 

1.  1  -  J.  6.  1  -  f .  11.  2-\.  16.  2  -  §. 

2.  1  -  J.  7.  1  -  |.  12.  3  -  |.  17.  2  -  i. 

3.  1  -  f .  8.  2  -  £.  13.  3  -  f .  18.  2  -  |. 

4.  1--J.  9.  2-|.  14.  4-£.  19.  3-f. 
5.1-f.  10.  2-  f.  15.  2-.J.  20.  4- f. 

21.  How  much  is  9  yd.  —  f  yd.  ? 

22.  If  I  have  $6  and  spend  $f ,  how  much  have  I  left  ? 

23.  If  from  5  Ib.  I  take  f  lb.,  what  is  the  remainder  ? 

24.  If  a  kite  string  440  ft.  long  shrinks  f  ft.,  how  long 
is  it  then  ? 

25.  If  from  a  12-foot  stick  we  saw  off  f  ft.,  what  is  then 
the  length  ? 


64.   Integers  minus  Fractions 


1.  10  -f. 

6.  13  -  f  . 

11.  30  -^. 

16.  46- 

2.  12-$. 

7.  17  -  f  . 

12.  32  -|. 

17.  52  - 

3.  14  -  ^ 

8.  18  -f. 

13.  25  -f 

18.  53- 

4.  12-£. 

9.  20  -  f  . 

14.  28-1. 

19.  58- 

5.  15  -|. 

10.  22  -  f  . 

15.  41  -|. 

20.  59  - 

21.  If  a  merchant  sells  f  yd.  of  velvet  from  a  piece  that 
contains  48  yd.,  how  much  has  he  left  ? 

22.  A  dealer  having  38  gallons  of  milk  sold  20  gallons 
and  then  \  gallon.    How  much  had  he  left  ? 

23.  A  man  having  $12  paid  a  quarter  of  a  dollar  for  eggs 
and  half  a  dollar  for  butter.    How  much  money  did  he 
then  have  ? 

24.  A  lady  having  a  piece  of  cloth  2\  yd.  long  sewed  on 
3^  yd.  more.   She  then  turned  in  |  yd.  at  one  end.   How  long 
was  the  piece  then  ? 


1.  lf-1. 

5.  li  -  f  . 

9. 

2.  If  -  i- 

6.   1J  -  f 

10. 

3.  H-f. 

7.  2i  -|. 

11. 

4.  U  -  i. 

8.  2|  -  I. 

12. 

SUBTRACTION  33 

65.   Mixed  Numbers  minus  Fractions 

To  subtract  a  fraction  from  a  mixed  number  proceed  as  follows : 
-  |  =  3|  -  |,  and  this  equals  21/-  -  I,  or  2f. 

-1.         13.  5^-i. 
-  |.         14.  6|  -  i. 

|.         15.  1\  -  V. 

l.        16.  7£  -  f . 

17.  What  number  must  be  added  to  2  to  make  5  ?   to  £ 
to  make  5|  ? 

18.  What  number  must  be  added  to  |  to  make  5^  ?   to  £ 
to  make  5^  ? 

19.  If  a  l|-inch  plank  is  dressed  down  to  1^  in.,  how 
much  is  taken  off? 

20.  If  from  a  beam  16±  in.  long  £  in.  is  sawed  off  from 
one  end  and  f  in.  from  the  other  end,  how  long  will  it  be  ? 

66.   Mixed  Numbers 

To  subtract  2|  from  5|  mentally,  first  subtract  2  and  then  |,  think- 
ing "  3|  -  f  =  3f  -  f,  or  3f ."    State  only  the  answer. 

J.  2|-li.  5.  5|-3|.  9.  3£-2£.  13.  5|  -  3|. 

2.  21  -  If.  6.  2|  -  1$.  10.  31  -  2^.  14.  64  -  3fi. 

3.  3|  -  If.  7.  3|  -  1*.  11.  3i  -  2|.  15.  6f  -  3|. 

4.  4|  -  2J.  8.  4J  -  2|.  12.  4|  -  2|.  16.  6J  -  4|. 

17.  What  remains  if  ^  yd.  is  taken  from  2^  yd.? 

18.  What  is  the  difference  between  |  yd.  and  3£  yd.  ? 

19.  From  7|  take  the  sum  of  J  and  £. 

20.  From  6£  take  the  sum  of  f  and  £. 

21.  From  6^  take  the  sum  of  1  and  | ;  then  subtract  ^. 

22.  What  number  must  be  added  to  |  to  make  4 £  ?   to 
make  4£  ? 

23.  What  number  must  be  added  to  the  sum  of  2£  and  ^ 
to  make  the  sum  of  2    and     ? 


34  COMMON  FRACTIONS 

67.   Review 

1.  How  far  around  a  triangle  1\  in.  on  a  side  ? 

2.  How  far  around  a  square  2^  in.  on  a  side  ? 

3.  How  far  around  a  square  room  15  ft.  on  a  side  ? 

4.  How  many  eighths  in  a  quarter  ?   in  a  half  ?    in  one  ? 

5.  What  is  the  sum  of  \  mi.,  \  mi.,  \  mi.,  and  1  mi.  ? 

6.  What  is  the  sum  of  f  in.  and  \  in.  ?    To  this  add  f  in. 

7.  How  much  is  two  dollars  and  a  half  less  a  dollar 
and  three  quarters  ? 

8.  If  you  cut  3^  in.  from  a  stick  5^  in.  long,  how  much 
is  left  ? 

9.  Prom  a  |-inch  board  \  in.  is  planed  off.    What  is  now 
the  thickness  ? 

10.  A  plank  1  \  in.  thick  has  a  £-inch  board  placed  on  top 
of  it.   What  is  the  combined  thickness  ? 

11.  A  3i-inch  hem  has  a  f-inch  strip  of  insertion  added. 
What  is  now  the  width  ? 

12.  At  28/  a  dozen,  what  will  2  dozen  eggs  and  15/ 
worth  of  celery  cost? 

13.  The  three  sides  of  a  triangle  are  2£  in.,  2^  in.,  and 
2^  in.    What  is  the  perimeter  ? 

14.  At  12^/  a  yard,  what  will  2  yd.  of  ribbon  and  a  4-cent 
spool  of  thread  cost  ? 

15.  At  16/  a  pound,  what  will  3  Ib.  of  meat  and  a  10-cent 
can  of  tomatoes  cost  ? 

16.  At  36/  a  pound,  what  will  2  Ib.  of  butter  and  15/ 
worth  of  cheese  cost? 

17.  The  perimeter  of  a  triangle  is  9  in.,  and  two  of  the 
sides  are  each  3^  in.    How  long  is  the  third  side  ? 

18.  What  additional  width  must  be  sewed  on  a  strip  of 
carpet  |  yd.  wide  to  make  it  1^  yd.  wide  ? 

19.  A  room  is  22^  ft.  long  and  15^  ft.  wide.  What  is  the 
sum  of  the  length  and  width  ?   What  is  the  perimeter  ? 


MULTIPLICATION  35 

68.    Multiplication.   By  Integers 

Multiplying  the  numerator  multiplies  a  fraction,  thus  : 


.      2      2x2 

V    V           — 

4 

2X5          5     ' 

3V 

1.  2  x  i 

5.  2  X  f  . 

9.  5  x  *. 

13.  2  x  f  . 

2.  2  x  i. 

6.   2  X  f  • 

10.  3  x  f 

14.  4  x  £. 

3.  3  x  £. 

7.  3  x  f  . 

11.  5  x  f 

15.  5  x  ^. 

4.  3  x  f 

8.  2  x  f  . 

12.  4  x  f 

16.  4  x  f  . 

17.  What  is  the  combined  thickness  of  three  pieces  of 
wood  each  ^  in.  thick  ? 

18.  If  each  side  of  a  5-sided  figure  is  £•  in.,  what  is  the 
perimeter  ? 

19.  What  is  the  sum  of  f  and  f  ?    How  much  is  2  x  $  ? 

20.  To  the  sum  of  what  four  fractions  is  4  x  §  equal  ? 

21.  To  the  sum  of  what  three  fractions  is  3  x  f  equal  ?   ' 

69.   By  Integers.   Reduction 

Multiplying  the  numerator,  or  dividing  the  denominator,  multiplies  a 
fraction,  thus  : 

2  X  -  =  -  ,  or 
4      4 

1.  2  X  i. 

2.  2  X  i- 

3.  2  x  f. 

4.  2  x  f 

17.  If  a  book  is  |  in.  thick,  how  thick  will  a  pile  of  8 
such  books  be  ?    of  4  such  books  ?    of  2  such  books  ? 

18.  If  a  pencil  is  f  in.  thick,  how  wide  a  space  will  2  such 
pencils  occupy  when  placed  side  by  side  ?   3  such  pencils  ? 
4  such  pencils  ?    8  such  pencils  ? 

19.  If  a  board  is  £  in.  thick,  how  thick  will  a  pile  of  2  such 
boards  be,  one  on  top  of  the  other  ?    4  such  boards  ?    6  such 
boards  ?   8  such  boards  ? 


«      \Ji     —    •          Xl.lOUf     — 

SI 

8          $    ' 

4 

5.  3  x  *. 

9.   2  x  f  . 

13.  4x|. 

6.  3x*. 

10.   2  x  |. 

14.  2  x  |. 

7.  5  x  }. 

11.  4xf. 

15.  3x|. 

8.  9  x  4. 

12.  4  x  |. 

16.  6  x  |. 

36  COMMON  FRACTIONS 

70.   Multiplication.   By  Unit  Fractions 

1.  £  of  4.  7.  i  of  40.  13.  i  of  24.  19.  £  of  45. 

2.  i  of  6.  8.  J.  of  50.  14.  £  of  32.  20.  $  of  63. 

3.  £  of  10.  9.  |  of  20.  15.  |  of  40.  21.  £  of  20. 

4.  ^  of  16.  10.  i  of  24.  16.  $  of  80.  22.  £  of  30. 

5.  J.  of  24.  11.  i  of  32.  17.  £  of  24.  23.  $  of  45. 

6.  J  of  30.  12.  £  of  44.  18.  £  of  33.  24.  £  of  75. 

25.  In  a  class  of  42,  half  are  boys.    How  many  girls  are 
there  ? 

26.  In  a  school  of  88  pupils  ^  are  in  the  fifth  grade.   How 
many  are  in  that  grade  ? 

27.  The  width  of  a  schoolroom  is  10  ft.  more  than  half 
the  length.    The  length  is  40  ft.    What  is  the  width  ? 

28.  The  perimeter  of  a  six-sided  figure  is  72  in.,  and  the 
sides  are  all  equal.    How  long  is  each  side  ? 

71.   By  Fractions 

Think  of  f  of  6  as  twice  }  of  6,  or  twice  2,  which  is  4.    State  only 
the  result. 


1. 

i  of 

9. 

6. 

|  of 

8. 

11. 

f  of 

24. 

16. 

| 

of  20. 

2. 

§of 

9. 

7. 

f  of 

12. 

12. 

f  of 

32. 

17. 

1 

of  24. 

3. 

*of 

15. 

8. 

|  of 

20. 

13. 

*of 

15. 

18. 

of  12. 

4. 

§of 

18. 

9. 

|of 

16. 

14. 

f  of 

15. 

19. 

1 

of  14. 

5. 

iof 

8. 

10. 

I  of 

16. 

15. 

f  of 

15. 

20. 

» 

of  14. 

21.  It  is  16  mi.  to  a  certain  place,  and  |  as  far  to  another 
place.    How  far  is  it  to  the  second  place  ? 

22.  If  a  boy  is  48  in.  tall,  and  his  sister  is  £  as  tall,  how 
tall  is  she  ? 

23.  If  a  horse  and  carriage  cost  $240,  and  the  horse  cost 
|  of  the  total,  how  much  did  the  carriage  cost  ? 

24.  If  a  city  building-lot  is  96  ft.  deep  and  |  as  wide,  how 
wide  is  it  ? 


MULTIPLICATION  37 

72.   By  Fractions 

1.  *  of  27.  6.  a  of  24.  11.  f  of  40.  16.  f  of  35. 

2.  §  of  27.  7.  i  of  40.  12.  I  of  40.  17.  £  of  30. 

3.  £  of  33.  8.  |  of  40.  13.  £  of  35.  18.  f  of  30. 

4.  §  of  33.  9.  £  of  40.  14.  f  of  35.  19.  }  of  21. 

5.  i  of  24.  10.  |  of  40.  15.  a  of  35.  20.  f  of  21. 

21.  At  48/  a  yard,  what  will  f  yd.  of  cloth  cost  ? 

22.  At  36/  a  yard,  what  will  a  yd.  of  cloth  cost  ? 

23.  At  24/  a  pound,  what  will  f  Ib.  of  figs  cost  ? 

24.  At  $120  an  acre,  what  will  i  acre  of  land  cost  ?  |  acre  ? 

25.  At  $160  an  acre,  what  will  |  of  an  acre  of  land  cost  ? 

26.  If  one  side  of  a  triangle  is  f  of  the  perimeter,  and 
the  perimeter  is  96  in.,  how  long  is  this  side  ? 

27.  If  a  man  weighs  180  Ib.  and  his  son  weighs  $  as 
much,  how  much  does  his  son  weigh  ? 

73.   Mixed  Numbers  by  Integers 

In  multiplying  2|  by  3  mentally,  it  is  better  to  multiply  first  the  2 
and  then  the  J.    3  x  2£  =  6f,  or  7.    Also,  7  x  5f  =  35  +  3,  or  38. 

1.  2  x  If          6.  4  x  3f         11.  4  x  2f  16.  5  x  4f 

2.2x2i.          7.4x5|.         12.  4x5f  17.  4  x  If. 

3.  2  x  7f          8.  4  x  1|.         13.  5  x  If  18.  4  x  2a. 

4.  4  x  li.          9.  2  x  If         14.  5  x  2f  19.  8  x  If. 

5.  4  x  If        10.  2  x  3f         15.  5  x  3i.  20.  8  x  2|. 
•^21.  At  $3^  each,  what  will  4  desks  cost  ? 

S  22.  At  $3^  each,  what  will  4  chairs  cost  ? 
-  23.  At  $3f  each,  what  will  4  tables  cost  ? 
s  24.  At  $2|  each,  what  will  a  dozen  lamps  cost  ? 

25.  If  a  strip  of  cloth  is  \\  yd.  wide,  how  wide  is  a  piece 
made  of  10  strips  ? 

26.  If  a  book  is  1|  in.  thick,  how  high  will  a  pile  of  4 
such  books  be  ?    of  8  such  books  ? 


38  COMMON  FRACTIONS 

74.  Multiplication.   Whole  by  Mixed  Numbers 

In  multiplying  by  a  mixed  number,  first  multiply  by  the  integer, 
thus  :  2|  times  8  is  2  x  8  and  \  of  8,  or  16  +  4,  or  20. 


i:  i 

ix 

4. 

6.  2 

:£  X 

6. 

11. 

5£  X 

10. 

16. 

2| 

Xl2. 

2.  1 

ix 

6. 

7.  2 

'k  x 

10. 

12. 

4^X 

20. 

17. 

2i 

X8. 

3.  1 

i  x 

10. 

8.  5 

'£  X 

20. 

13. 

e>\    v 

^¥  X 

8. 

18. 

2| 

x8. 

4.  1 

1  x 

24. 

9.  f 

>£  x 

4. 

14. 

91  v 

^j  A 

12. 

19. 

2| 

x8. 

5.  2 

'i  X 

4. 

10.  4 

^x 

4. 

15. 

2f  x 

8. 

20. 

x8. 

21.  At  20  /  a  pound,  what  will  2|  Ib.  of  meat  cost  ? 

22.  At  22/  a  pound,  what  will  2  J  Ib.  of  meat  cost  ? 

23.  At  50/  a  yard,  what  will  1^  yd.  of  cloth  cost? 

24.  At  $36  a  dozen,  what  will  \\  doz.  hats  cost  ? 

25.  At  72/  a  yard,  what  will  2J  yd.  of  cloth  cost? 

26.  At  24/  a  dozen,  what  will  2  doz.  eggs  cost  ?   2J  doz.  ? 
\  doz.  ? 

75.   Multiplication.   Fractions  by  Fractions 

To  take  -  of  - ,  multiply  thus :    \     —  =  —    To  take  -  of   - , 
35  3x5      15  3         4 


i  of  f  16.  §  of  f . 
^  of  ^.  17.  §  of  f. 
£  of  J.  18.  |  of  4. 
^  of  i.  19.  |  of  f 
i  of  ^.  20.  f  of  f 

21.  Find  the  value  of  \  of  § ;  of  \  of  §  of  f . 

22.  How  much  is  \  of  three  quarters  of  a  yard  ? 

23.  How  much  is  §  of  three  quarters  of  a  dollar  ? 

24.  If  you  live  f  mi.  from  the  schoolhouse,  and  I  live 
half  as  far,  how  far  away  do  I  live  ? 

25.  If  a  man  owns  J  of  an  acre  of  land  and  sells  f  of 
what  he  owns,  how  much  does  he  sell  ? 


cancel, 

2 

thus  :    -  o 

^    2' 

2 

1. 

ioff. 

6.  ^ 

off. 

11. 

2. 

4  of  f. 

7-  4 

off. 

12. 

3. 

*off. 

8.  4 

off 

13. 

4. 

*off. 

9-  i 

of  f  . 

14. 

5. 

i  of*. 

10.  J 

off. 

15. 

DIVISION  39 

76.   Division.   Fractions  by  Integers 

To  divide  a  fraction  'by  an  integer,  we  divide  the  numerator  if  pos- 
sible, thus :   |  -^  2  =  §. 

1.  §-5-2.         6.  f  -^3.         11.  if-*- 4.         16.  §£-5-9. 
2.|-5-3.         7.  |  -s-  5.          12.  £§  -5-  6.         17.  §f  -5-  5. 

3.  f-5-4.         8.  $-5-2.         13.   1-1-5-3.         18.  |f -s- 5. 

4.  |  -5-  2.         9.  §  -5-  2.         14.  if  -5-  5.         19.  |f  -j-  7. 

5.  $-5-2.       10.  £§-5-3.       15.  §£-5-3.      ,  20.  ff  -*- 11. 

21.  Reduce  lj  to  halves  and  then  divide  by  3. 

22.  Reduce  1|  to  thirds  and  then  divide  by  5. 

23.  In  the  same  way,  divide  If  by  3  ;  also  by  9.- 

24.  In  the  same  way,  divide  3£  by  4 ;  also  by  8. 

25.  In  the  same  way,  divide  2|  by  11 ;  also  3J  by  7. 

26.  In  the  same  way,  divide  4|  by  2 ;  also  by  7 ;  also 
by  14. 

77.   Fractions  by  Integers 

When  it  is  impossible  to  divide  the  numerator,  multiply  the  de- 

2 

444  42 

nominator,  thus  :    -  -=-  3  =  —  Also  -  -r-  6  = =  — 

5  15  5  5  x  0      15 

3 

1.  £  -5-  3.  6.    f  -5-  2.  11.    1-5-6.  16.    T25  -5-  4. 

2.  £-5-2.         7.  f-5-2.         12.  §-*-8.  17.^-5-6. 

3.  £  -s-  4.         8.  |  -*-  3.          13.  f  -5-  4.  18.  /6  -5- 10. 

4.  J  -H  2.         9.  §  -f-  4.         14.  t\  -H  6.         19.  ^  -5- 14. 

5.  1-5-2.       10.  f  -5-  6.         15.  f  -5- 16.         20.  ^  -*- 18. 

21.  Reduce  1J  to  halves  and  then  divide  by  4. 

22.  If  it  is  |  mi.  around  a  square  field,  what  is  the  length 
of  each  side  ? 

23.  If  a  man  goes  |  mi.  in  4  min.  on  his  bicycle,  at  what 
rate  is  he  traveling  per  minute  ? 

24.  If  a  train  travels  3^  mi.  in  4  min.,  what  is  its  rate 
per  minute  ? 


40  COMMON  FRACTIONS 

78.   Integers  by  Unit  Fractions 


1.  1  -J-  \. 

5.  2-*-$. 

9.  6  -s-  J. 

13.  15  -=-  f 

2.  2-s-i. 

6.  7-s-£. 

10.  5  -*-  £. 

14.  12  -5-  J. 

3.  5  -s-  £. 

7.  1  -H  i. 

11.    5-5-f 

15.  11-s-J. 

4.  l-i-£. 

8.  2-i. 

12.  8  -=-  f 

16.  10^-TV 

17.  How  many  half  inches  in  3  in.  ? 

18.  How  many  quarter  dollars  in  $8  ?  in  $10  ?    in  $12  ? 

19.  How  m#ny  thirds  of  a  yard  in  4  yd.  ?   How  many 
feet  in  4  yd.  ? 

20.  How  many  twelfths  of  a  foot  in  4  ft.  ?    How  many 
inches  in  4  ft.  ? 

21.  If  a  running  track  is  \  mi.  around,  how  many  times 
would  you  have  to  go  round  it  to  travel  2  mi.  ?    3  mi.  ? 

22.  How  many  twelfths  of  an  inch  in  1  in.  ?    in  3  in.  ?    in 
10  in.  ?  in  a  foot  ? 

79.   Integers  by  Fractions 

3 

23v721  'iRvTS 

Think  of  7  -  -  as  —  —  ,  or  —  ,  or  101.  Think  of  15  -5-  -  as  2JL£?  , 

Q  9  9  81 

or  24. 

13.  2  -s-  J. 

14.  3  -=-  |. 

15.  6  H-  |. 

16.  14  -=-  ?. 

17.  How  many  times  is  |  contained  in  3  ? 

18.  If  a  book  is  £  in.  thick,  how  many  books  in  a  pile 
3  in.  high  ? 

19.  If  a  book  "is  |  in.  thick,  how  many  books  in  a  pile 
3  in.  high  ? 

20.  If  a  book  is  |  in.  thick,  how  many  books  in  a  pile 
7  in.  high  ?    14  in.  high  ?    21  in.  high  ? 

21.  How  many  layers  of  veneer  must  be  glued  together 
to  make  a  piece  1  in.  thick,  allowing  ^  in.  for  each  layer  ? 


1       1    -!-   2 
1.     -L  —  3. 

5.  5^-§. 

Q     2  _s_  2 

».     ^  -r-  f  . 

2.  2-s-f. 

6.  6  -=-  |. 

10.    3  -i-  I  . 

3.  2-s-|. 

7.  2  -«-  i. 

11.  6  -*-  f. 

4.  2-4-f. 

8.  2n-|. 

12.  6-v-f. 

DIVISION  41 

80.   Fractions  by  Fractions 

,535;*         5 
Think  of  -  -s-  -  as  -  x  -  >  or  -  • 

8      4       $     3         6    . 
2 

1.  £  -=-  4.  5.  £  -s-  4.  9.  4  -5-  4-  13.  4  -*•  |. 

2.  4  -5-  4.  6.  4  H-  |.  10.  f  -r-  4.  14.  §  -«- 1. 

3.  ^-=-4.  7.  4-*-f.  11.  4-5-4.  15.  -|-v-|. 

4.  4  -H  TV  8.  4-5-4.  12.  4-5-4.  16.  §  -H  $. 

17.  How  many  quarter  dollars  in  a  half  dollar  ? 

18.  How  many  eighths  of  an  inch  in  4  in.  ?    in  £  in.  ? 
in  |  in.  ? 

19.  A  ruler  is  marked  in  thirty-seconds  of  an  inch.  How 
many  of  these  lengths  in  i  in.  ?  in  4  in.  ?  in  £  in.  ?  in  £  in.  ? 

20.  How  many  thirty-sixths  of  a  yard  in  4  yd.?    in  4  yd. ? 
in  §  yd.  ?  What  does  this  mean,  expressed  in  inches  or  feet  ? 

81.   Mixed  Numbers 

3     2 

394 

Think  of  <H  H-  -  as  -  x  - ,  or  6. 
4       ?     3 

1.  l^  -5-  4.        4.  H  -*-  TV-        7.  l-i-  -~  T\.        10.  1£  ^-  ^ 

2.  li-s-i.        5.  li-i-|.          8.24-5-4.          11.14-5-$. 

3.  14  -5-  4.        6.  14  H-  |.          9.  24  -=-  f .          12.  IJ  -5-  -|. 

13.  How  many  quarter  dollars  in  $3^  ?    in  $5^  ? 

14.  A  real  estate  dealer  has  |  of  an  acre  of  land  divided 
into  lots  of  4  of  an  acre  each.    How  many  lots  has  he  ? 

15.  He  also  has  another  piece  containing  2|  acres  divided 
into  lots  of  \  of  an  acre  each.    How  many  lots  in  this  piece  ? 

16.  He  has  also  another  piece  containing  1\  acres  divided 
into  lots  of  4  of  an  acre  each.    How  many  lots  in  this  piece  ? 

17.  A  cooking  recipe  calls  for  £  pt.  of  cream  to  each 
person,  and  I  take  34  pt.  of  cream.    I  have  enough  cream 
for  how  many  persons  ? 


42  ALIQUOT  PARTS 

III.    ALIQUOT  PARTS 

82.  Multiplying  by  5 

Since  5  =  10  -f-  2,  to  multiply  by  5  we  may  annex  a  cipher  and 
divide  by  2,  when  this  is  easier.   Thus  5  x  48  =  ^  of  480  =  240. 

1.  5  x  14.  5.  5  x  28.  9.  5  x  32.  13.  5  x  51. 

2.  5  x  16.  6.  5  x  44.  10.  5  x  34.  14.  5  x  54. 

3.  5  x  18.  7.  5  x  82.  11.  5  x  36.  15.  5  x  73. 

4.  5  x  24.  8.  5  x  84.  12.  5  x  38.  16.  5  x  77. 

17.  At  42/  each,  what  will  5  books  cost? 

18.  At  24/  a  dozen,  what  will  5  dozen  eggs  cost  ? 

19.  At  22/  a  pound,  what  will  5  pounds  of  meat  cost  ? 

20.  At  $82  an  acre,  what  will  5  acres  of  land  cost  ? 

21.  Try  multiplying  58  by  5,  mentally,  in  the  way  you 
used  to  do,  and  in  the  way  here  shown.    Which  is  easier  ? 

83.  Multiplying  by  25 

Since  25  =  100  H-  4,  to  multiply  by  25  we  may  annex  two  ciphers 
and  divide  by  4.    Thus  25  x  16  =  1600  -^  4  =  400. 

1.  25  x  8.       4.  25  x  24.       7.  25  x  44.       10.  25  x  36. 

2.  25  x  6.        5.  25  x  28.        8.  25  x  48.        11.  25  x  80. 

3.  25  x  12.      6.  25  x  40.        9.  25  x  32.        12.  25  x  84. 

13.  At  32/  a  pound,  what  will  25  Ib.  of  butter  cost  ? 

14.  At  36/  each,  what  will  25  books  cost  ? 

15.  At  $48  each,  what  will  25  cows  cost  ? 

16.  At  $120  each,  what  will  25  horses  cost  ? 

17.  At  $28  each,  what  will  25  sets  of  furniture  cost? 

18.  At  $16  each,  what  will  25  overcoats  cost  ? 

19.  At  44/  each,  what  will  railway  tickets  for  a  party  of 
25  cost  ? 

20.  At   22/   a   pound,   what  will   25  Ib.  of  figs  cost  ? 
(Divide  $22  by  4  or  divide  it  by  2  twice.) 


ALIQUOT  PARTS  OF  $1  43 

84.   Aliquot  Parts  of  $1 

50?  =  £  of  $1.  33$?  =  $  of  $1. 

25/  =  £  of  $1.  20/  =  J  of  $1. 

12$?  =  i  of  $1.  10/  =  TV  of  $1. 

It  is  easier  to  multiply  |  than  to  multiply  50,  \  than  25,  £  than  12  1, 
and  so  on.  Therefore  4  x  \Z$f  =  4  x  $£  =  $£  ;  36  x  25^  =  36  x  $$• 
=  -?9  ;  12  x  33ijz>  =  12  x  $^  =  $4. 


1.  6x50/.    6.12x25?.     11.12x12$?.    16.  15x33j/. 

2.  8  x  50/.    7.  16  x  25/.     12.  24  x  12£/.    17.  5  x  20/. 

3.  7  x  50/.    8.  24  x  25/.     13.  6  x  33£^.      18.  15  x  20/. 

4.  9  x  50/.    9.  8  x  12i/.     14.  9  x  33£/.      19.  25  x  20/. 

5.  8x25/.  10.  16xl2i/.  15.  12x33^/.    20.  35x20/. 

21.  At  25/  each,  what  will  7  fishing  poles  cost  ? 

22.  At  12^/  a  yard,  what  will  32  yd.  of  cloth  cost  ? 

23.  At  20/  a  yard,  what  will  160  yd.  of  cloth  cost  ? 

85.   Aliquot  Parts  of  $1 

In  a  case  like  that  of  7  x  33^,  we  have  : 

7  x  33i(*  =  7  x  ft  =  $21. 


1.  5  x  25?.    4.  6  x  25?.        7.  11  x  12$?.    10. 

2.  7  x  25?.    5.  9  x  12$?.      8.  15  x  12£/.     11.  10  x  33$ /. 

3.  9  x  25/.    6.  10  x  12$/.    9.  5  x  33$/.       12.  11  x  33$?. 

13.  At  25/  each,  what  will  6  baseballs  cost  ? 

14.  At  S?  a  quart,  what  will  25  qt.  of  berries  cost  ? 

15.  At  12$?  a  quart,  what  will  6  qt.  of  berries  cost  ? 

16.  At  33$?  each,  what  will  6  books  cost  ?   9  books  ? 

17.  At  20?  each,  what  will  55  books  cost  ?  75  books  ? 

18.  At  3?  a  foot,  how  much  will  33 $  ft.  of  molding  cost? 
(33$  x  3?  is  the  same  as  J-§&  of  3/.) 

19.  At  6?  a  yard,  how  much  will  33 $  yd.  of  ribbon  cost  ? 

20.  At  60/  a  yard,  how  much  will  33$  yd.  of  carpet  cost  ? 


44  DENOMINATE  NUMBERS 

IV.   DENOMINATE  NUMBERS 

86.  Measures  of  Length 

1.  3  ft.  =  ?  in.  9.  1  mi.  =  ?  ft.  17.  2  yd.  =  ?  in. 

2.  5  ft.  =  ?  in.  10.  2^  ft.  =  ?  in.  18.  £  yd.  =  ?  in. 

3.  7  ft.  =  ?  in.  11.  2J  ft.  =  ?  in.  19.  1J.  yd.  =  ?  in. 

4.  3  yd.  =  ?  ft.  12.  If  ft.  =  ?  in.  20.  |  yd.  =  ?  in. 

5.  5  yd.  =  ?  ft.  13.  4J  yd.  =  ?  ft.  21.  f  yd.  =  ?  in. 

6.  7  yd.  =  ?  ft.  14.  5£  yd.  =  ?  ft.  22.  If  yd.  =  ?  in. 

7.  1  rd.  =  ?  ft.  15.  6f  yd.  =  ?  ft.  23.  $  yd.  =  ?  in. 

8.  2  rd.  =  ?  ft.  16.  1  yd.  =  ?  in.  24.  §  yd.  =  ?  in. 

25.  How  many  feet  long  do  you  think  your  schoolroom 
is  ?   How  many  yards  is  this  ? 

26.  How  many  feet  long  do  you  think  the  teacher's  desk 
is  ?   How  many  inches  is  this  ? 

87.  Measures  of  Length 

1.  27  in.  =  ?  ft.      4.  36  in.  =  ?  ft.         7.  72  in.  =  ?  ft. 

2.  27  in.  =  ?  yd.     5.  2  x  36  in.  =  ?  in.   8.  36  +  18  =  ? 

3.  36  in.  =  ?  yd.     6.  72  in.  =  ?  yd.        9.  54  in.  =  ?  yd. 

10.  How  much  is  £  of  52  ?    £  of  528  ?    J  of  5280  ?   How 
many  feet  in  £  mi.  ? 

11.  Brussels  carpet  is  f  yd.  wide.    How  many  inches 
wide  is  it  ? 

12.  How  does  §  yd.  compare  in  length  with  2  ft.  ?   with 
24  in.  ? 

13.  Which  is  the  longest,  f  yd.,  2  ft.  4  in.,  or  2J  ft.  ?    If 
two  are  the  same,  which  two  ? 

14.  A  lady  wishes  27  in.  of  cloth  to  finish  a  garment. 
What  part  of  a  yard  does  she  need  ? 

15.  A  lady  wishes  48  in.  of  cloth  to  finish  some  work. 
Express  this  length  as  yards. 


SQUARE  MEASURE  45 

88.  Square  Measure 

1.  1  sq.  ft.    =  ?  sq.  in.  5.  £  sq.  ft.    =  ?  sq.  in. 

2.  1  sq.  yd.  =  ?  sq.  ft.  6.  $  sq.  yd.  =  ?  sq.  ft. 

3.  1  sq.  ft.    =  ?  sq.  yd.  7.  2  sq.  ft.    =  ?  sq.  in. 

4.  3  sq.  ft.    =  ?  sq.  yd.  8.  £  sq.  yd.  =  ?  sq.  ft. 

9.  The  page  of  a  book  is  7  in.  by  3  in.    What  is  its  area  ? 

10.  The  page  of  a  book  is  8  in.  by  4|  in.  What  is  its  area  ? 

11.  A  lot  is  8|  yd.  by  20  yd.    What  is  its  area? 

12.  A  floor  is  16  ft.  long  and  10£  ft.  wide.  What  is  its  area? 

13.  A  table  top  is  4  ft.  long  and  a  yard  wide.    What  is 
its  area  in  square  feet  ? 

14.  A  field  is  25  rd.  long  and  20  rd.  wide.    What  is  its 
area  in  square  rods  ? 

15.  A  field  is  33£  rd.  long  and  30  rd.  wide.    What  is  its 
area  in  square  rods  ? 

89.  Square  Measure 

The  area  of  a  triangle  is  half  that  of  a  rectangle  of  the  same  base 
and  height.  The  area  of  a  triangle  whose  base  is  4  ft.  and  height  3  ft. 
is  \  of  4  x  3  sq.  ft. ,  or  6  sq.  ft. 

Find  the  areas  of  the  triangles  whose  bases  and  altitudes 
(heights)  are  given  as  follows : 

1.  4  ft.,  4  ft.  4.  2  in.,  10  in.  7.  2  in.,  2^  in. 

2.  5  ft.,  4  ft.  5.  3  in.,  5  in.  8.   1  in.,  2%  in. 

3.  6  in.,  3  in.  6.  5  ft.,  7  ft.  9.  3  in.,  1\  in. 

10.  WThich  has  the  greater  area,  a  square  7  in.  on  a  side, 
or  a  rectangle  4  in.  by  12  in.  ? 

11.  Which  has  the  greater  area,  a  square  that  is  9  in.  on 
a  side,  or  a  triangle  whose  base  is  16  in.  and  height  10  in.  ? 

12.  Which  has  the  greater  area,  a  triangle  whose  base  is 
15  in.  and  height  5  in.,  or  one  whose  base  is  10  in.  and 
height  1\  in.? 


46  DENOMINATE  NUMBERS 

90.   Cubic  Measure 

1.  1  cu.  ft.  =  ?  cu.  iii.  5.  2  cu.  yd.  =  ?  cu.  ft. 

2.  1  cu.  yd.  =  ?  cu.  ft.  6.  l£  cu.  yd.  =  ?  cu.  ft. 

3.  £  cu.  yd.  =  ?  cu.  ft.  7.  1J  cu.  yd.  =  ?  cu.  ft. 

4.  £  cu.  yd.  =  ?  cu.  ft.  8.  2£  cu.  yd.  =  ?  cu.  ft. 
9.  How  many  cubic  feet  in  a  room  20  ft.  long,  20  ft. 

wide,  and  10  ft.  high  ? 

10.  How  many  cubic  inches  in  a  box  5  in.  long,  4  in.  wide, 
and  3  in.  deep  ? 

11.  Does  a  box  that  is  20  in.  long,  10  in.  wide,  and  10  in. 
deep,  contain  more  than  or  less  than  1  cu.  ft.  ?' 

12.  How  many  cubic  inches  in  a  box  that  is  8  in.  long, 
3^  in.  wide,  and  1  in.  deep  ? 

13.  How  many  cubic  feet  in  a  box  that  is  6  ft.  long,  4J  ft. 
wide,  and  2  ft.  deep  ? 

91.  Weight 

1.  1  T.  =  ?  Ib.         7.  5  Ib.  =  ?  oz.  13.  |  Ib.  =  ?  oz. 

2.  2  T.  =  ?  Ib.         8.  10  Ib.  =  ?  oz.  14.  £  Ib.  =  ?  oz. 

3.  1  Ib.  =  ?  oz.        9.  25  Ib.  =  ?  oz.  15.  1$  Ib.  =  ?  oz. 

4.  2  Ib.  =  ?  oz.  10.  i  Ib.  =  ?  oz.  16.  li  Ib.  =  ?  oz. 

5.  ^  T.  =  ?  Ib.  11.  J  Ib.  =  ?  oz.  17.  If  Ib.  =  ?  oz. 

6.  1$  T.  =  ?  Ib.  12.  |  Ib.  =  ?  oz.  18.  1$  Ib.  =  ?  oz. 

19.  How  much  is  3£  x  12/  ? 

20.  How  much  will  3  Ib.  8  oz.  of  meat  cost  at  20/  a 
pound  ? 

21.  Instead  of  speaking  of  4  Ib.  4  oz.  of  meat,  what  will 
the  dealer  state  as  the  weight  ? 

22.  Instead  of  speaking  of  37  Ib.  4  oz.  of  butter,  what 
will  a  dealer  state  as  the  weight  ? 

23.  Instead  of  speaking  of  your  weight  as  75  Ib.  12  oz., 
how  will  you  state  it  ? 


CAPACITY  47 

92.   Dry  Measure 

1.  8  qt.  =  ?  pk.  10.  3|  pk.  =  ?  qt. 

2.  2  qt.  =  ?  pk.  11.  51  pk.  =  ?  qt. 

3.  4  qt.  =  ?  pk.  12.  8  pk.  =  ?  bu. 

4.  16  qt.  =  ?  pk.  13.  12  pk.  =  ?  bu. 

5.  12  qt.  =  ?  pk.  14.  16  pk.  =  ?  bu. 

6.  24  qt.  =  ?  pk.  15.  18  pk.  =  ?  bu. 

7.  48  qt.  =  ?  pk.  16.  5  bu.  =  ?  pk. 

8.  32  qt.  =  ?  pk.  17.  2^  bu.  =  ?  pk. 

9.  6  pk.  =  ?  qt.  18.  1  bu.  =  ?  qt. 

19.  At  90/  a  bushel,  what  will  3  bu.  of  wheat  cost  ? 

20.  At  $1  a  bushel,  what  will  8  bu.  2  pk.  of  wheat  cost  ? 
Instead  of  8  bu.  2  pk.,  what  will  this  be  called  ? 

21.  At  $1^  a  bushel,  what  will  16  bu.  of  wheat  cost? 
Instead  of  $1|,  what  will  this  be  called  ? 

93.   Liquid  Measure 

1.  2  pt.  =  ?  qt.  10.  20  qt.  =  ?  pt. 

2.  1  pt.  =  ?  qt.  11.  £'  qt.  =  ?  pt. 

3.  4  pt.  =  ?  qt.  12.  1£  qt.  =  ?  pt. 

4.  8  pt.  =  ?  qt.  13.  5£  qt.  =  ?  pt. 

5.  6  pt.  =  ?  qt.  14.  3  gal.  =  ?  qt. 

6.  7  pt.  =  ?  qt.  15.  6  gal.  =  ?  qt. 

7.  30  pt.  =  ?  qt.  16.  8  qt.  =  ?  gal. 

8.  3  qt.  =  ?  pt.  17.  3|  gal.  =  ?  qt. 

9.  5  qt.  =  ?  pt.  18.  10  qt.  =  ?  gal. 

19.  At  60/  a  quart,  what  will  £  pt.  of  cream  cost  ? 

20.  At  32/  a  gallon,  what  will  3  qt.  of  milk  cost  ? 

21.  At  48/  a  quart,  what  will  a  pint  of  cream  cost  ? 

22.  A  dealer  has  a  gallon  of  cream.  What  is  this  worth 
at  30/  a  pint  ? 

23.  How  many  pints  in  a  gallon  ?   in  2  gal.?    in  l£  gal.? 


48  DENOMINATE  NUMBERS 

94.   Addition 

1.  2  ft.  3  in.  4.  3  ft.  4  in.  7.  3  yd.  27  in. 
3       7                          3        8  2  9 

2.  3  ft.  6  in.  5.  4  ft.  3  in.  8.  2  ft.  9  in. 
5       5                          5       9  3        9 

3.  3  yd.  10  in.            6.  2  yd.  2  ft.  9.  3  yd.  2  ft. 
2           8                      3 1_  2         2 

10.  5  sq.  ft.  100  sq.  in.                      11.  3  cu.  yd.  20  cu.  ft. 
2  44  2 7 

12.  A  lady  buys  27  yd.  18  in.  of  cloth  to  add  to  18  yd. 
18  in.  that  she  has.    How  many  yards  has  she  now  ? 

13.  A  lady  buys  33J  yd.  of  cloth  and  finds  that  she  needs 
4J  yd.  more.    She  decides  to  buy  18  in.  more  than  this. 
How  much  does  she  buy  in  all  ? 

14.  A  man  wishes  to  send  an   article  by  express.    It 
weighs  7  Ib.  13  oz.,  and  he  finds  that  the  wrapping  paper 
weighs  12  oz.    What  is  the  total  weight  of  the  package  ? 

15.  A  man  has  worked  2  wk.  5  da.  on  a  job,  and  must 
work  3  wk.  4  da.  longer  to  finish  it.    Allowing  six  working 
days  to  a  week,  how  long  will  it  take  to  do  the  whole  work  ? 

16.  The  opening  in  a  picture  frame  has  an  area  of  2  sq.  ft. 
37  sq.  in.,  and  the  frame  itself  has  an  area  of  78  sq.  in. 
What  is  the  total  area  of  the  frame  and  opening  ? 

17.  A  man  sells  52J  yd.  of  carpet.    The  next  day  the  pur- 
chaser buys  3|  yd.  more.    He  loses  18  in.  by  sewing  and 
matching.    How  many  yards  in  the  carpet  as  laid  ? 

18.  A  contractor  excavated  48^  cu.  yd.  of  earth  one  day 
and  51  £  cu.  yd.  the  next  day.    How  many  cubic  feet  did  he 
excavate  in  the  two  days  together? 


ADDITION                                         49 

95.   Addition 

1. 

1 

ft.  4  in. 

5.  8 

Ib. 

10  oz. 

9.  8  rd. 

10ft. 

2 

6 

.2 

14 

3 

6 

2. 

3 

ft.  8  in. 

6.  5 

Ib. 

11  oz. 

10.  7  bu. 

2 

pk. 

2 

4 

2 

8 

2 

2 

3. 

7 

ft.  9  in. 

7.  7 

yd. 

2  ft. 

11.  7  gal 

.  1 

qt. 

3 

4 

8 

1 

5 

3 

4. 

2 

Ib.  3  oz. 

8.  9 

yd. 

2  ft. 

12.  9  gal 

.  3 

qt. 

4 

9 

6 

2 

8 

-3 

13.  A  table  is  3  ft.  8  in.  long  and  2  ft.  6  in.  wide.  What 
is  the  sum  of  its  length  and  breadth  ? 

14.  A  table  is  4  ft.  7  in.  long  and  3  ft.  6  in.  wide.    What 
is  the  perimeter  of  the  table  ? 

15.  A  room  is  18  ft.  9  in.  long  and  12  ft.  6  in.  wide. 
What  is  the  perimeter  of  the  room  ? 

16.  A  lamp  weighing  3  Ib.  9  oz.  contains  13  oz.  of  oil. 
What  is  the  combined  weight  of  the  lamp  and  the  oil  ? 

17.  A  rug  is  3  yd.  2  in.  long  and  1  yd.  10  in.  wide.    How 
many  yards  of  braid  will  it  take  to  bind  it,  allowing  12  in. 
for  waste  ? 

18.  A  piece  of  fence  extends  8  rd.  8^  ft.  along  a  field, 
and  3J  rd.  more  must  be  built.    What  will  be  the  total 
length  when  it  is  finished  ? 

19.  A  man  has  worked  7  wk.  2  da.  on  a  job  and  must 
work  4  wk.  3  da.  longer  to  finish  it.    Allowing  six  working 
days  to  a  week,  how  long  will  it  take  to  do  the  whole  work  ? 

20.  A  carpenter  has  built  10  rd.  8-]-  ft.  of  fence,  and  has 
to  build  2^  rd.  more  to  complete  one  side  of  a  square.   What 
will  be  the  perimeter  of  the  square  ? 


50  DENOMINATE  NUMBERS 

96.    Subtraction 


1. 

2. 

3. 

4 

2 

ft. 

11  in. 

7 

4. 
5. 
6. 

8 

hr.  15 
.20 

min. 

7. 
8. 
9. 

8 
2 

Ib. 

5  oz. 

6 

4 
1 

Ib. 

14  oz. 

8 

16  bu.  2 
3 

pk. 

5 
2 

rd. 

10ft. 
BJ 

5 
2 

gal 

.  3  qt. 
1 

4 
1 

wk.  3 
5 

da. 

G 
4 

mi. 

35  rd. 

17 

10.  5  sq.  ft.    0  sq.  in.                        11.  3  cu.  yd.    3  cu.  ft. 
1 44  1 20 

12.  A  rug  3  yd.  6  in.  long  is  placed  on  a  floor  5  yd.  4  in. 
long.    How  much  of  the  length  of  the  floor  is  not  covered  ? 

13.  A  man  borrowed  some  money  2  mo.  12  da.  ago,  for 
6  mo.    How  long  after  to-day  before  the  money  is  due  ? 

14.  A  boy  weighs  75^  Ib.,  and  has  gained  6  Ib.  8  oz.  since 
his  last  birthday.    How  much  did  he  then  weigh  ? 

15.  A  girl  weighs  67  Ib.  4  oz.,  and  the  last  time  she  was 
weighed  her  weight  was  65  Ib.  12  oz.    How  much  has  she 
gained  ? 

16.  A  man  weighed  162  Ib.  4  oz.  on  January  1,  and  the 
next  time  he  was  weighed  he  had  lost  3^  Ib.    How  much 
did  he  then  weigh  ? 

17.  A  lady  having  purchased  14£  yd.  of  cloth  finds  that 
she  should  have  bought  17  yd.  18  in.    How  much  more 
should  she  buy  ? 

18.  A  lady  having  purchased  16^  yd.  of  cloth  finds  she 
has  27  in.  too  much.    How  much  did  she  really  need  ? 

19.  A  lady  purchased  27^  yd.  of  cloth  for  a  dress,  and 
then  found  she  could  have  made  it  with  25|  yd.    How  many 
inches  did  she  waste  ? 


SUBTRACTION  51 

97.   Subtraction 

1.  19  ft.  9  in.          5.  10  Ib.  10  oz.  9.  4  rd.  £  ft. 

2        6  13  7_ 

2.  18  ft.  7  in.          6.  21  Ib.  10  oz.          10.  21  mi.  70  rd. 
_5 7_  1        13  16 

3.  10  ft.  6  in.          7.  12  yd.  1  ft.  11.  4  mi.  20  rd. 

8  2  40 

4.  12  ft.  6  in.          8.  32  yd.  1  ft.  12.  12  mi.  1  ft. 

1        8  1         2  4       81 

13.  A  boy  is  11  yr.  4  mo.  old,  and  his  sister  is  exactly 
2  yr.  6  mo.  younger  than  he.    How  old  is  his  sister  ? 

14.  A  man  had  to  travel  6£  mi.,  and  has  already  traveled 
2  mi.  160  rd.    How  far  has  he  still  to  travel  ? 

15.  A  room  is  3  ft.  8  in.  longer  than  it  is  wide.    It  is 
17  ft.  long.    How  wide  is  it  ? 

16.  A  building  is  31  ft.  8  in.  high.    The  lowest  story  is 
10  ft.  9  in.  high.    How  high  is  the  building  above  the  lowest 
story  ? 

17.  A  rug  6  ft.  8  in.  wide  lies  on  a  floor  14  ft.  4  in.  wide. 
How  much  of  the  width  of  the  floor  is  not  covered  ? 

18.  An  express  package  weighs  17  Ib.  4  oz.    It  consists 
of  a  box  and  some  goods,  the  goods  weighing  13  Ib.  8  oz. 
How  much  does  the  box  weigh  ? 

19.  A  man  is  37  yr.  8  mo.  old,  his  son  is  12  yr.  2  mo.  old, 
and  his  daughter  10  yr.  8  mo.  old.    How  much  older  is  the 
man  than  his  son  ?   than  his  daughter  ? 

20.  A  man  is  36  yr.  6  mo.  old,  his  wife  is  32  yr.  4  mo. 
old,  and  his  son  11  yr.  3  mo.  old.    How  much  older  than 
the  son  is  the  father  ?    is  the  mother  ? 


52  DENOMINATE  NUMBERS 

98.   Multiplication 

Express  as  inches,  and  then  as  feet : 
1.  2x6  in.        2.  3x4  in.      3.  2x12  in.      4.  4x9  in. 

Express  as  ounces,  and  then  as  pounds  : 
5.  4  x  4  oz.        6.  8  x  2  oz.      7.  4  x  8  oz.        8.  2  x  16  oz. 

Express  as  quarts,  and  then  as  gallons : 
9.  2x2qt.      10.  8x1  qt.    11    2x8qt.      12.  4x2qt. 

Express  as  feet  or  inches,  and  then  as  yards : 

13.  3x2  ft.       14.  9x2  ft.     15.  3x12  in.    16.  2x18  in. 

Express  as  quarts  or  pecks,  and  then  as  bushels : 

17.  2xl6qt.    18.  4x8qt.     19.  4x4pk.     20.   8x4  pk. 

Multiply  : 

21.  1  ft.  3  in.  by  2.  27.  2  Ib.  9  oz.  by  2. 

22.  1  ft.  6  in.  by  2.  28.  3  yd.  1  ft.  by  3. 

23.  1  ft  9  in.  by  2.  29.  3  yd.  2  ft.  by  6. 

24.  3  ft.  8  in.  by  3.  30.  2  gal.  2  qt.  by  2. 

25.  3  ft  7  in.  by  4.  31.  2  gal.  2  qt.  by  8. 

26.  2  Ib.  8  oz.  by  2.  32.  8  qt.  1  pt.  by  8. 

33.  Find  the  perimeter  of  a  square  4  ft.  3  in.  on  a  side. 

34.  If  a  square  flower  bed  is  3  ft.  6  in.  on  a  side,  how 
long  will  be  a  string  stretched  around  the  perimeter  ? 

35.  One  side  of  a  square  is  8  in.    Express  the  perimeter 
in  inches  ;  in  feet  and  inches ;  in  feet  and  a  fraction. 

36.  If  a  triangular  flower  bed  is  3  ft.  4  in.  on  a  side,  and 
we  wish  to  put  a  wire  fence  around  it  of  three  strands,  how 
much  wire  must  we  have,  allowing  5  ft.  extra  for  all  the 
fastenings  ? 


DIVISION  53 

99.   Division 

Express  as  inches,  and  then  as  feet  : 
1.  24  in.  -s-2.     2.  48in.-s-2.      3.  72in.-s-2.      4.  72in.-=-3. 

Express  as  ounces,  and  then  as  pbunds  : 

.^-2.     6.  48oz.H-3.      7.  64oz.-=-2.      8.  64oz.-=-4. 


Express  as  quarts,  and  then  as  gallons  : 
9.  16qt.-s-2.  10.  32qt.-5-8.    11.  64qt.-s-8.    12.  48  qt.-s-12. 

Express  as  feet  or  inches,  and  then  as  yards  : 

13.  12  ft.  -j-2.    14.  60  ft.  -=-2.    15.  9  ft.  -5-3.       16.  72in.-s-2. 

Express  as  quarts  or  pecks,  and  then  as  bushels  : 

17.  64qt.-s-2.  18.  16pk.-*-4.  19.  32pk.+4.  20.  64pk.-=-8. 

Divide  : 

21.  10  ft.  4  in.  -=-  2.  27.  64  mi.  16  rd.  -*-  8. 

22.  18  ft.  6  in.  -f-  6.  28.  1  ft.  6  in.  -5-  3. 

23.  16  yd.  2  ft.  --  2.  29.  2  ft.  6  in.  -=-  10. 

24.  25  Ib.  15  oz.  -=-  5.  30.  2  Ib.  8  oz.  -4-  20. 

25.  21  gal.  7  pt.  H-  7.  31.  66  ft.  -5-  11  ft. 

26.  81  bu.  18  qt.  -5-  9.  32.  42  Ib.  -5-  21  Ib. 

33.  How  many  times  is  1  ft.  8  in.  contained  in  5  ft.  ? 

34.  If  a  book  covers  32  sq.  in.,  how  many  such  books 
will  it  take  to  cover  96  sq.  in.  ?    320  sq.  in.  ? 

35.  If  a  wheel  is  9  ft.  in  circumference,  how  many  revo- 
lutions will  it  make  in  going  108  ft.  ? 

36.  If  a  gallon  of  ice  cream  is  allowed  for  24  persons, 
what  part  of  a  pint  is  allowed  to  each  ? 

37.  The  perimeter  of  a  triangle  is  72  in.  and  the  sides 
are  all  equal.    Express  each  side  in  inches  ;  in  feet. 


54  REVIEW 

100.   Review 

1.99  +  8.         7.75-17.  13.4x22.  19.  108  -=-9. 

2.  33  +  8.         8.  52  -  28.  14.  6  x  35.  20.  132  H-  6. 

3.  98  +  20.       9.  $l-72/.  15.  7x27.  21.  63-8. 

4.  76  +  35.  10.  $l-54/.  16.  8x33.  22.  52 -f- 7. 
5.73  +  42.  11.  $2-28^.  17.14x7.  23.  43 -=-6. 
6.63  +  28.  12.  $2-37/.  18.16x8.  24.80-9. 

Reduce  to  lowest  terms  : 

25.  f.  26.  f.  27.  f.  28.  £. 

Reduce  to  improper  fractions  : 

29.  If.  30.  31.  31.  5£.  32.  3|. 

Perform  the  operations  indicated  : 

33.  i  +  f  41.  i  -  f  49.  3  -  £.  57.  3  x  2£. 

34.  £  +  f .  42.  i  -  J.  50.  4  -  f .  58.  4  x  2|. 

35.  |  +  f  43.  f  -  £.  51.  5  -  f .  59.  5  x  3§. 

36.  f  +  |.  44.  I  -  J.  52.  7  -  f .  60.  8  x  2|. 

37.  3+|.  45.  |  -  |.  53.  ±  of  36.  61.  J-  of  |. 

38.  3  +  5.  46.  11.  _  £.  54.  |  Of  44.  62.  §  of  f . 

39.  3  +  |.  47.  21  -  i.  55.  §  of  48.  63.  £  of  §. 

40.  1£  +  f  48.  2^  -  f  56.  |  of  64.  64.  f  of  J. 

65.  How  many  inches  in  |  yd.  ?    in  J  of  |  yd.  ? 

66.  How  many  pints  in  2  gal.  ?    in  £  gal.  ?   in  3^  gal.  ? 

67.  At  24/  a  pound,  how  much  will  3£  Ib.  of  meat  cost  ? 

68.  At  32^  a  pound,  how  much  will  2i  Ib.  of  butter  cost  ? 

69.  If  I  go  to  the  grocer's  and  spend  37/  for  sugar,  44^ 
for  butter,  and  22/  for  cheese,  how  much  do  I  spend  for 
all  ?    How  much  change  is  due  from  $1.10  ? 

70.  If  I  spend  62/,  35/,  20/,  and  8/,  how  much  do  I 
spend  in  all  ?    Express  the  result  as  cents  ;  as  dollars  and. 
cents ;  as  dollars  and  a  fraction. 


CHAPTEE  II 

I.    OPERATIONS  WITH  INTEGERS 
1.   Adding  2's  and  3's 


1. 

32  +  2. 

5. 

86- 

h20. 

9. 

92  +  3. 

13. 

66 

+  30. 

2. 

45  +  2 

6. 

73- 

h20. 

10. 

78+3. 

14. 

83 

+  30. 

3. 

178  + 

2. 

7. 

97- 

h20. 

11. 

297 

+  3. 

15. 

75 

+  30. 

4. 

164  + 

2. 

8. 

89- 

[-20. 

12. 

384 

+  3. 

16. 

99 

+  30. 

17.  How  much  is  $117  and  $3  ?    149  ft.  and  30  ft.  ? 

18.  How  much  is  239  ft.  and  3  ft.  ?    239  ft.  and  20  ft.  ? 

19.  How  much  is  $229  and  $2?    $222  and  $9?   269 
and  10  and  2  ?   269  and  12  ?    263  and  19  ? 

20.  How  much  is  179  ft.  and  3  ft.  ?    173  ft.  and  9  ft.  ? 
173  and  10  and  9?    173  and  19  ?    273  and  39  ? 

2.   Adding  4's  and  5's 


1. 

72  +  4 

5. 

95 

+  40. 

9. 

96  +  5. 

13. 

45 

4- 

50. 

2. 

46  +  4 

6. 

83 

+  40. 

10. 

77  +  5. 

14. 

32 

+ 

50. 

3. 

394  + 

4. 

7. 

97 

+  40. 

11. 

264  +  5. 

15. 

97 

+ 

50. 

4. 

488  + 

4. 

8. 

99 

+  40. 

12. 

798  +  5. 

16. 

89 

+ 

50. 

17.  How  much  is  $176  and  $5  ?    $298  and  $4  ? 

18.  How  much  is  $297  and  "$4  ?    $399  and  $5  ? 

19.  How  much  is  198  ft.  and  5  ft.  ?    198  ft.  and  10  ft.  ? 
298  ft.  and  15  ft.  ? 

20.  If  a  man  weighs  149  Ib.  and  carries  a  50-pound  box, 
how  much  do  the  man  and  box  together  weigh?    What 
would  this  be  if  the  box  weighed  51  Ib.  ?    55  Ib.  ? 

55 


56  INTEGERS 

3.   Adding  6's  and  7's 


1. 

98  +  6. 

5. 

72 

+  60. 

9. 

83  +  7 

13. 

94 

+ 

70. 

2. 

96  +  6. 

6. 

97 

+  60. 

10. 

96  +  7 

14. 

72 

+ 

70. 

3. 

263  +  6. 

7. 

95 

+  60. 

11. 

297  + 

7. 

15. 

95 

+ 

70. 

4. 

384  +  6. 

8. 

99 

+  60. 

12. 

488  + 

7. 

16. 

89 

+ 

70. 

17.  Add  $197  and  $6 ;  $196  and  $7. 

18.  Add  $187  and  $20 ;  $187  and  $23. 

19.  How  much  is  89  mi.  and  7  mi.  and  6  mi.  ? 

20.  If  you  have  39  marbles  and  6  marbles,  how  many 
marbles  have  you? 

21.  If  a  man  has  $297  in  the  bank  and  deposits  $7  one 
week  and  $60  the  next  week,  how  much  does  he  then  have  ? 

22.  If  a  farmer  has  193  acres  of  land  and  buys  10  more 
from  one  man,  7  from  another,  and  60  from  another,  how 
many  acres  does  he  then  have  ? 

4.   Adding  8's  and  9's 


1. 

99  +  8. 

5. 

88 

+  80. 

9. 

99  +  9 

13. 

98 

+ 

90. 

2. 

95  +  8. 

6. 

93 

+  80. 

10. 

92  +  9 

14. 

75 

+ 

90. 

3. 

297  +  8. 

7. 

76 

+  80. 

11. 

484  + 

9. 

15. 

86 

+ 

90. 

4. 

462  +  8. 

8. 

94 

+  80. 

12. 

677  + 

9. 

16. 

63 

+ 

90. 

17.  Add  $288  and  $8  and  $90. 

18.  Add  $148  and  $20  and  $8. 

19.  Add  $167  and  $10  and  $9. 

20.  How  does  the  sum  of   $398  and  $9  compare  with 
that  of  $399  and  $8  ? 

21.  How  does  the  sum  of  36  marbles  and  9  marbles  com- 
pare with  that  of  38  marbles  and  7  marbles  ? 

22.  If  a  man  pays  $89  for  clothes  and  $8  for  shoes  and 
$4  for  a  hat,  what  is  the  total  ? 

23.  The  three  sides  of  a  triangle  are  14  in.,  9  in.,  and  8  in. 
Express  the  sum  in  inches ;  in  feet  and  a  fraction. 


ADDITION  57 

5.  Adding  Two-figure  Numbers 

To  add  27  to  46  mentally,  it  is  a  little  easier  first  to  add  20  and 
then  to  add  7,  thinking  66,  73.    State  aloud  only  73. 

1.  40  +  30.  5.  50  +  40.  9.  60  +  70.  13.  80  +  50. 

2.  46  +  30.  6.  57  +  40.  10.  64  +  70.  14.  86  +  50. 

3.  46  +  34.  7.  57  +  43.  11.  64  +  75.  15.  86  +  57. 

4.  46  +  39.  8.  57  +  48.  12.  64  +  79.  16.  86  +  59. 

17.  How  much  is  27  in.  and  25  in.  ? 

18.  If  you  have  76/  and  71/,  how  much  have  you  ? 

19.  What  is  the  sum  of  38  and  8  and  14  ?    (First  take 
38  +  8.) 

20.  If  I  pay  65/  for  a  book  and  75/  for  some  note  paper, 
how  much  do  I  pay  for  both  ? 

21.  If  I  buy  at  a  grocery  store  goods  costing  36/,  28/, 
and  36/,  what  is  the  total  cost  ? 

6.  Adding  Two-figure  Numbers 

1.  80  +  70.  5.  70  +  30.  9.  50  +  90.  13.  60  +  80. 

2.  87  +  70.  6.  78  +  30.  10.  57  +  90.  14.  68  +  80. 

3.  87  +  76.  7.  78  +  33.  11.  57  +  95.  15.  68  +  89. 

4.  87  +  79.  8.  78  +  37.  12.  57  +  98.  16.  68  +  88. 

17.  125  +  30.  19.  125  +  39.  21.  $175  +  $46. 

18.  125  +  37.  20.  175  +  40.  22.  $175  +  $48. 

23.  What  is  the  sum  of  $235  and  $38  ? 

24.  A  farmer  having  175  acres  of  land  buys  36  acres 
more.    How  many  acres  does  he  then  have  ? 

25.  If  the  distance  from  here  to  a  certain  place  called  X 
is  158  mi.,  and  another  place  called  Y  is  63  mi.  beyond 
X,  how  far  is  Y  from  here  ? 

26.  If  there  are  38  pupils  in  the  fifth  grade  of  a  certain, 
school,  32  in  the  sixth  grade,  and  30  in  the  seventh  grade, 
how  many  pupils  are  there  in  the  three  grades  together  ? 


58  INTEGERS 

.     7.   Adding  Two-figure  Numbers 

1.  28  +  14.  5.  38  +  32.  9.  86  +  25.  13,  98  +  46. 

2.  34  +  19.  6.  58  +  27.  10.  95  +  35.  14.  79  +  48. 

3.  46  +  27.  7.  87  +  38.  11.  97  +  15.  15.  94  +  73. 

4.  29  +  13.  8.  59  +  26.  12.  87  +  44.  16.  78  +  82. 

17.  How  much  is  99/  and  16^  ?    95/  and  17/  ? 

18.  A   school   paid   $94  for   new   blackboards,   $7   for 
erasers,  and  $4  for  crayons.  How  much  did  it  pay  for  all  ? 

19.  If  a  man  pays  $135  for  a  horse,  $8  for  delivering  it 
at  his  home,  and  $3  for  feed,  what  is  the  total  ? 

20.  A  lady  paid  47/  for  cloth,  26/  for  braid,  and  8/  for 
thread.    What  was  the  total  ? 

21.  A  lady  paid  36/  for  braid,  18/  for  needles,  15/  for 
thread,  5X  for  car  fare,  and  26/  for  postage  stamps.    How 
much  did  she  pay  in  all  ? 

8.   Adding  Two-figure  Numbers 

1.  70  +  56.  5.  80  +  68.  9.  90  +  35.  13.  60  +  56. 

2.  75  +  56.  6.  87  +  68.  10.  96  +  35.  14.  69  +  56. 

3.  75  +  55.  7.  87  +  63.  11.  96  +  34.  15.  69  +  51. 

4.  75  +  57.  8.  87  +  66.  12.  96  +  37.  16.  69  +  58. 

17.  Add  $265  and  $80;  $265  and  $86. 

18.  If  a  rectangle  is  135  ft.  long  and  65  ft.  wide,  what  is 
the  perimeter  ? 

19.  If  a  school  spends  $135  for  repairs  and  $78  for  fuel, 
what  is  the  total  ? 

20.  If  a  man  has  68  cows  and  17  sheep,  how  many  head 
of  stock  does  he  have  ? 

21.  If  a  man  has  $275  in  the  bank  and  deposits  $18 
more,  how  much  does  he  then  have  ? 

22.  If  a  man  has  $260  in  the  bank  and  deposits  $50  more 
to-day  and  $75  more  to-morrow,  how  much  will  he  then  have  ? 


SUBTRACTION  59 

9.    Subtraction 


1.  42-8. 
2.  36  -  7. 
3.  28  -  9. 
4.  52-7. 

5.  23-4. 
6.  34-6. 
7.  41  -  7. 
8.  73  -  8. 

9.  57  -  9. 
10.  26  -  8. 
11.  35-7. 
12.  52  -  6. 

13.  31  -  8. 
14.  53-7. 
15.  46  -  7. 
16.  37  -  8. 

17.  If  a  strip  8  in.  wide  is  cut  from  a  strip  of  carpet  |  yd. 
wide,  how  many  inches  wide  is  the  remainder  ? 

18.  If  a  town  is  72  mi.  from  here,  and  another  town  is 
8  mi.  this  side  of  it,  how  far  is  this  other  town  from  here  ? 

19.  What  is  the  base  of  a  rectangle  whose  perimeter  is 
44  in.  and  whose  altitude  is  8  in.  ? 

20.  What  must  be  added  to  9  to  make  61  ?  What  must 
be  subtracted  from  61  to  make  8  ? 

21.  How  much  must  be  added  to  48  ft.  of  rope  to  make 
55  ft.  ?   to  make  53  ft.  ?   to  make  51  ft.  ? 

10.    Subtraction 

To  subtract  15  from  37  it  is  best  to  think  of  37  -  10  -  5,  or  27  -  5. 
State  only  the  result,  22. 

1.  37  -  15.  5.  82  -  31.      .9.  76  -  23.      13.  93  -  52. 

2.  48  -  12.  6.  65  -  23.      10.  87  -  45.      14.  96  -  66. 

3.  54  -  32.  7.  77  -  25.      11.  96  -  31.      15.  85  -  75. 

4.  69  -  27.  8.  84  -  33.      12.  88  -  44.      16.  75  -  42. 
17.  125  -  20.  18.  235  -  100.            19.  325  -  125. 

20.  What  must  be  added  to  22  to  make  77  ? 

21.  What  must  be  subtracted  from  85  to  make  60  ? 

22.  What  number  is  12  less  than  42  ?  12  less  than  72  ? 

23.  If  I  have  $1.75  and  spend  32/,  how  much  have  I  left? 

24.  If  a  playground  is  185  ft.  long  and  72  ft.  wide,  how 
much  greater  is  the  length  than  the  width  ? 

25.  If  a  farmer  having  78  head  of  cattle  should  sell  36 
head,  how  many  head  would  he  have  left? 


60  INTEGERS 

11.    Subtraction 

To  subtract  48  from  83  mentally,  it  is  easier  first  to  subtract  40,  and 
then  to  subtract  8,  thinking  43,  35.    State  aloud  only  35. 


1. 

83- 

30. 

5. 

64 

-40. 

9. 

87 

-60. 

13. 

56 

-20. 

2. 

83- 

35. 

6. 

64 

-47. 

10. 

87 

-68. 

14. 

56 

-29. 

3. 

72- 

20. 

7. 

91 

-50. 

11. 

65 

-20. 

15. 

80 

-30. 

4. 

72- 

28. 

8. 

91 

-52. 

12. 

65 

-27. 

16. 

80 

-32. 

17. 

135  -  60. 

18.  135 

— 

65. 

19. 

135 

-69. 

20.  How  much  more  than  $45  is  $82  ? 

21.  How  much  less  than  $73  is  $45  ? 

22.  What  number  must  be  added  to  27  in.  to  make  54  in.? 

23.  If  a  man  has  $525  in  the  bank,  and  takes  out  $100, 
how  much  will  he  have  ?  Instead  of  $100,  suppose  he  takes 
out  $125  ?  suppose  he  takes  out  $127  ? 

12.   Subtraction 

1.  50  -  20.  5.  70  -  40.  9.  51  -  32.  13.  86  -  29. 

2.  53  -  20.  6.  72  -  40.  10.  63  -  24.  14.  85  -  27. 

3.  53  -  23.  7.  72  -  42.  11.  65  -  28.  15.  92  -  36. 

4.  53  -  28.  8.  72  -  49.  12.  84  -  58.  16.  94  -  47. 

17.  What  number  must  be  added  to  28  make  252? 

18.  How  much  more  is  $120  than  $30  ?   than  $35  ? 

19.  How  much  more  is  $125  than  $40  ?  than  $47  ? 

20.  What  number  must  be  subtracted  from  72  ft.  to  make 
36  ft.  ? 

21.  The  perimeter  of  a  triangle  is  31  in.,  and  two  sides 
are  13  in.  and  9  in.    What  is  the  third  side  ? 

22.  If  you  have  made  a  score  of  57  in  a  game  and  some 
one  else  has  made  39,  how  much  are  you  ahead  ? 

23.  If  in  a  running  match  one  boy  has  run  111  yd.  and 
another  has  run  98  yd.,  the  first  boy  is  how  far  ahead  ? 


SUBTRACTION                                     6 

13.    Subtraction 

1. 

81- 

50. 

5. 

63 

-40. 

9. 

45- 

20. 

13. 

77- 

58. 

2. 

81- 

53. 

6. 

63 

-48. 

10. 

45- 

29. 

14. 

77- 

49. 

3. 

72- 

30. 

7. 

54 

-20. 

11. 

66- 

40. 

15. 

80- 

52. 

4. 

72- 

39. 

8. 

54 

-27. 

12. 

66- 

48. 

16. 

83- 

55. 

17. 

$105 

-  $40.         18.  $105  -  $45. 

19. 

$105  -  $46 

20.  What  is  the  difference  between  35  bu.  and  100  bu.  ? 

21.  What  is  the  difference  between  48  ft.  and  148  ft.  ? 
48  ft.  and  144  ft.  ?  48  ft.  and  134  ft.  ? 

22.  If  a  retail  dealer  owes  a  wholesale  dealer  $425  and 
pays  him  $125,  how  much  does  he  still  owe  ? 

23.  If  a  merchant  sold  $130  worth  of  goods  one  day, 
$98  worth  the  next  day,  and  $89  worth  the  next  day,  his 
sales  for  the  first  day  were  how  much  greater  than  for  the 
second  ?    than  for  the  third  ? 

14.   Subtracting  from  100 

To  subtract  48  from  100,  subtract  40  +  8  from  90  +  10,  thinking 
50  +  2  =  52.    State  aloud  only  52. 

1.  100  -  26.  5.  100  -  47.  9.  100  -  53.  13.  100  -  81. 

2.  100  -  58.  6.  100  -  54.  10.  100  -  69.  14.  100  -  66. 
3.100-25.  7.100-82.  11.100-18.  15.100-78. 
4.  100  -  36.  8.  100  -  61.  12.  100  -  38.  16.  100  -  92. 

Find  the  change  due  from  $1  on  purchases  of: 

17.  16/.  21.  33/.  25.  75/.  29.  29/.  33.  57/. 

18.  37/.  22.  40/.  26.  30/.  30.  95/.  34.  13/. 

19.  49/.  23.  62/.  27.  25/.  31.  85/.  35.  86/. 

20.  28/.  24.  88/.  28.  50/.  32-.  15/.  36.  46/. 

37.  How  much  is  100  ft.  —  68  ft.  ? 

38.  If  a  man  owes  $100  and  pays  $59,  how  much  does 
he  still  owe  ? 


62  INTEGERS 

15.   Subtracting  from  Hundreds 

In  subtracting  138  from  700,  think  of  700  as  600  +  90  +  10,  and 
subtract  from  left  to  right. 

1.  100-20.  5.  200-43.  9.  400-55.  13.  500-120. 

2.  100-26.  6.  200-69.  10.  400-38.  14.  500-125. 

3.  200-26.  7.  300-72.  11.  500-29.  15.  600-130. 

4.  200-57.  8.  300-47.  12.  500-78.  16.  600-135. 

17.  What  must  be  subtracted  from  $700  to  make  $138  ? 

18.  If  the  distance  from  Chicago  to  New  York  is  1000  mi., 
and  Detroit  is  256  mi.  from  Chicago,  how  far  is  Detroit 
from  New  York  by  this  route  ? 

19.  If  a  man  owes  $142  and  pays  two  $100  bills,  how 
much  change  is  due  him  ? 

20.  If  your  purchases  amount  to  $1.50,  50/,  25/,  and 
75/,  how  much  change  is  due  you  from  $10  ? 

16.    Making  Change 

For  the  method  of  making  change  see  page  12,  or  follow  the  plan 
of  Exercise  15  above. 

Find  the  change  due  from  $1  if  you  make  purchases  of: 
1.  72/.        2.  17/.        3.  26/.         4.  41/.        5.  83/. 

Find  the  change  due  from  $2  if  you  make  purchases  of: 
6.  $1.25.      7.  $1.36.      8.  $1.14.      9.  $1.50.   10.  $1.85. 

Find  the  change  due  from  $3  if  you  make  purchases  of: 
11.  $2.35.    12.  $2.48.    13.  $2.05.    14.  $2.27.   15.  $2.75. 

Find  the  change  due  from  $5  if  you  make  purchases  of: 

16.  $4.20.    17.  $4:35.    18.  $3.40.    19.  $2.80.   20.  $1.60. 

21.  How  much  is  $15  -$12.75  ? 

22.  How  much  is  $33  —  $21.70 .? 


MULTIPLICATION  63 

17.  Review  of  the  Table 

1.  4x4. 

2.  3  x  4. 

3.  2x7. 

4.  5x5. 

5.  3x3. 

6.  4x7. 

7.  7x7. 

29.  How  much  is  7  x  $9  ?    9  x  $7? 

30.  The  product  of  what  two  other  whole  numbers  equals 
the  product  of  4  and  9  ? 

31.  The  product  of  what  two  other  whole  numbers  equals 
the  product  of  8  and  7  ? 

32.  State  two  whole  numbers  whose  product  is  32.    Give 
as  many  different  answers  as  you  can. 

18.  Review  of  the  Table 


8.  2x4. 

15.  5x8. 

22.  5x7. 

9.  7x8. 

16.  4x5. 

23.  3x9. 

10.  6x6. 

17.  4x6. 

24.  9x6. 

11.  3x5. 

18.  8x8. 

25.  2x2. 

12.  6x7. 

19.  9x8. 

26.  3x8. 

13.  9x9. 

20.  3x6. 

27.  7x9. 

14.  2x3. 

21.  6x8. 

28.  4x9. 

1. 

9x 

7. 

9. 

8x 

4. 

17. 

3x 

7. 

25. 

9 

x5. 

2. 

7x 

2. 

10. 

6x 

2. 

18. 

8x 

9. 

26. 

8 

x6. 

3. 

8x 

2. 

11. 

4x 

3. 

19. 

6x 

9. 

27. 

9 

x4. 

4. 

6x 

5. 

12. 

3x 

2. 

20. 

2x 

8. 

28. 

8 

x5. 

5. 

6x 

3. 

13. 

5x 

6. 

21. 

2x 

9. 

29. 

8 

x3. 

6. 

7x 

4. 

14. 

8x 

7. 

22. 

2x 

5. 

30. 

7 

x6. 

7. 

5x 

3. 

15. 

2x 

6. 

23. 

4x 

8. 

31. 

(1 

X4. 

8. 

4x 

2. 

16. 

9x 

3. 

24. 

5x 

9. 

32. 

7. 

x3. 

33.  Of  what  two  whole  numbers  is  35  the  product?   49? 
21?   33? 

34.  Of  what  two  whole  numbers  is  55  the  product  ?    77  ? 
39?   51? 

35.  How  many  yards  of  cloth  can  I  buy,  and  at  what 
price,  so  that  the  cost  amounts  to  64/  ?    Give  as  many  dif- 
ferent answers  in  whole  numbers  as  you  can. 


64  INTEGERS 

19.   Two-figure  Multiplicand 

Think  of  4  x  21  as  80  +  4  ;  of  4  x  32  as  120  +  8,  beginning  at  the 
left  to  multiply. 

1.4x21.  6.5x21.  11.8x20.  16.7x61. 

2.  4  x  20.  7.  6  x  30.  12.  8  x  21.  17.  8  x  40. 

3.  4  x  30.  8.  6  x  31.  13.  2  x  50.  18.  8  x  41. 

4.  4  x  31.  9.  7  x  30.  14.  2  x  53.  19.  9  x  70. 

5.  5  x  20.  10.  7  x  31.  15.  7  x  60.  20.  9  x  71. 

21.  At  32/  a  yard,  what  will  4  yd.  of  cloth  cost  ? 

22.  At  62/  a  yard,  what  will  3  yd.  of  carpet  cost  ? 

23.  At   2/  each,  what   will  23   postage    stamps   cost? 
(Multiply  23  by  2,  although  when  you  give  an  explanation 
you  must  say  23  times  2/.) 

24.  At  5/  each,  what  will  31  postage  stamps  for  foreign 
letters  cost  ?  what  will  22  postage  stamps  cost  ? 

20.   Two-figure  Multiplicand 

Think  of  3  x  47  as  3  x  40  and  3  x  7,  or  120  +  21,  or  141.    State 
only  the  result. 

1.  3  x  30.          7.  4  x  23.        13.  6  x  30.        19.  7  x  62. 

2.  3  x  33.          8.  4  x  26.         14.  6  x  31.        20.  7  x  65. 

3.  3  x  34.          9.  5  x  40.         15.  6  x  33.        21.  9  x  20. 

4.  3  x  37.         10.  5  x  41.         16.  6  x  36.        22.  9  x  21. 

5.  4  x  20.         11.  5  x  42.        17.  7  x  60.        23.  8  x  30. 

6.  4  x  22.         12.  5  x  45.         18.  7  x  61.        24.  8  x  32. 

25.  At  36?  a  dozen,  what  will  6  doz.  oranges  cost  ? 

26.  At  32?  a  pound,  what  will  8  Ib.  of  butter  cost? 

27.  At  16/  a  jar,  what  will  7  jars  of  marmalade  cost  ? 

28.  At  $42  a  thousand,  what  will  6  thousand  feet  of 
lumber  cost  ? 

29.  At  $48  a  thousand,  what  will  9  thousand  feet  of 
lumber  cost? 


MULTIPLICATION  65 

21.  Multiplication 

1.  3  x  40.  6.  4  x  62.  11.  6  x  54.  16.  7  x  85. 

2.  3  x  43.  7.  4  x  65.  12.  6  x  55.  17.  9  x  50. 

3.  3  x  45.  8.  4  x  69.  13.  7  x  80.  18.  9  x  51. 

4.  3  x  49.  9.  6  x  50.  14.  7  x  81.  19.  9  x  52. 

5.  4  x  60.  10.  6  x  51.  15.  7  x  82.  20.  9  x  54. 

21.  At  $55  each,  what  will  8  head  of  cattle  cost? 

22.  At  $45  a  set,  what  will  4  sets  of  furniture  cost  ? 

23.  At  75/  a  dozen,  what  will  6  doz.  pencils  cost  ? 

24.  If  one  arithmetic  costs  45/,  how  much  will  6  arith- 
metics cost  ? 

25.  If  there  are  48  ft.  in  each  of  4  fishing  lines,  how 
many  feet  in  all  ? 

26.  If  you  have  37  marbles  and  some  one  else  has  three 
times  as  many,  how  many  marbles  has  he  ? 

22.  Multiplication 

1.  5  x  60. 

2.  5  x  67. 

3.  4  x  70. 

4.  4  x  73. 

5.  6  x  40. 

6.  6  x  47. 

25.  What  will  5  sets  of  furniture  cost  at  $30  ?    at  $32  ? 

26.  What  will  7  cows  cost  at  $40  ?    at  $42  ?    at  $44  ? 
at  $48  ?   at  $52  ? 

27.  What  will  9  office  desks  cost  at  $20  ?   at  $21  ?   at 
$22?   at  $26? 

28.  What  will  8  sets  of  dishes  cost  at  $20  ?   at  $21  ? 
at  $23  ?   at  $27  ? 

29.  What  will  be  the  total  cost  of  2  horses  at  $75  each 
and  3  cows  at  $42  each  ? 


7.  8  x  60. 

13.  7  x  60. 

19.  6  x  80. 

8.  8  x  64. 

14.  7  x  67. 

20.  6  x  84. 

9.  3x90. 

15.  9x50. 

21.  7  x  70. 

10.  3  x  96. 

16.  9x55. 

22.  7  x  72. 

11.  2x80. 

17.  4  x  40. 

23.  8  x  60. 

12.  2  x  88. 

18.  4x48. 

'    24.  6  x  36. 

66 


INTEGERS 


1.  2  x  33. 
2.  2x37. 
3.  3x23. 
4.  3  x  28. 

5.  4x42. 
6.  4x45. 
7.  5x31. 
8.  5  x  36. 

9.  6  x  72. 
10.  7x41. 
11.  7  x43. 
12.  6x71. 

23.   Multiplication 

13.  8x25. 

14.  8  x  27. 

15.  9x71. 

16.  9  x  73. 

17.  At  $6.70  each,  how  much  will  2  dictionaries  cost? 

18.  At  $140  each,  how  much  will  4  horses  cost  ? 

19.  At  $160  each,  how  much  will  3  carriages  cost  ? 

20.  At  35/  each,  how  much  must  a  school  pay  for  9 
text-books  ? 

21.  If  the  average  number  in  each  class  of  a  school  of  8 
grades  is  34,  what  is  the  total  number  in  school  ? 

22.  If  the  average  number  of  examples  in  each  of  7 
exercises   in   arithmetic   is   24,  how  many  examples   are 
there  in  all  the  7  exercises  ? 


24.   Cost  of  Purchases 


Find  the  cost  of  the  following : 

1.  4  bicycles  at  $32. 

2.  3  tables  at  $12. 

3.  5  plows  at  $22. 

4.  7  stoves  at  $32. 

5.  7  rugs  at  $22. 

6.  6  trunks  at  $23. 

7.  9  bedsteads  at  $22. 

8.  8  sofas  at  $32. 

9.  6  writing  desks  at  $21. 

10.  2  typewriters  at  $87. 

11.  8  pairs  of  lace  curtains 
at  $23. 

12.  5   suits  of  clothes  at 

at 


13.  6  carts  at  $52. 

14.  7  acres  of  land  at  $62. 

15.  5  sets  of  dishes  at  $33. 

16.  3  large  mirrors  at  $36. 

1 7.  4  sets  of  harness  at  $32. 

18.  8  watch  chains  at  $42. ' 

19.  9  watches  at  $42. 

20.  8  overcoats  at  $25. 

21.  9  doz.  hats  at  $33. 

22.  5  show  cases  at  $82. 

23.  6  sewing  machines  at 
t3. 

24.  4  doz.  window  frames 
$43. 


DIVISION  67 

25.   Dividing  by  2 


1. 

6-1-2, 

6. 

32- 

2. 

11. 

80 

-=-2. 

16. 

640- 

2. 

2. 

66  -H 

2. 

7. 

34- 

2. 

12. 

86 

H-2. 

17. 

340- 

2. 

3. 

64- 

2. 

8. 

50-5- 

2. 

13. 

88 

—  2. 

18. 

560-=- 

2. 

4. 

82- 

2m 

9. 

54- 

2. 

14. 

90 

-2. 

19. 

808  -s- 

0 

5. 

30- 

2. 

10. 

56- 

2. 

15. 

92 

H-2. 

20. 

980  H- 

2. 

1. 

How 

many  2-cent  stain 

.ps  can  you  bm 

r  for  | 

11.40? 

22.  How  many  newspapers  can  you.  buy  for  7S/,  at  2/ 
each? 

23.  At  2/  a  mile,  how  far  can  you  travel  for  $1.60  ?  how 
far  for  $1.70? 

24.  A  class  of  54  marched  out  of  the  room  two  by  two. 
How  many  couples  were  there  ? 

25.  In  a  class  of  78  pupils  there  are  as  many  boys  as  girls. 
How  many  are  there  of  each  ? 

26.   Dividing  by  3 

1.  9  -=-  3.  6.  69  -T-  3.  11.  78  -  3.  16.  960  -=-  3. 

2.  90  -  3.  7.  36  -  3.  12.  81  -  3.  17.  609  H-  3. 

3.  96  -  3.  8.  45  -  3.  13.  51  -  3.  18.  750  -  3. 

4.  60-^3.  9.  75-3.  14.  54-3.  19.  810  —  3. 

5.  63  -T-  3.  10.  72-3.  15.  57-3.  20.  570 -=- 3. 

21.  How  many  yards  are  there  in  66  ft.  ? 

22.  How  many  yards  are  there  in  93  ft.  ? 

23.  How  many  yards  are  there  in  360  ft.  ? 

24.  At  $3  each,  how  many  hats  can  be  bought  for  $48  ? 

25.  At  $3  each,  how  many  curtains  can  be  bought  for  $87  ? 

26.  At  3/  each,  how  many  pencils  can  be  bought  for  72/  ? 

27.  At  3/  each,  how  many  yards  of  ribbon  can  be  bought 
for  84/? 

28.  The  perimeter  of  a  triangle  is  150  ft.  and  the  sides 
are  all  equal.    How  many  feet  are  there  in  each  side  ? 


1. 

8n-4. 

7. 

50 

-H5. 

13. 

60 

-t- 

6. 

19. 

2. 

80 

_s_  4_ 

8. 

60 

-5. 

14. 

66 

-i- 

6. 

20. 

3. 

84 

-f-4. 

9. 

75 

+  5. 

15. 

72 

4. 

6. 

21. 

4. 

40 

-4. 

10. 

80 

-^5. 

16. 

48 

— 

6. 

22. 

5. 

48 

-^4. 

11. 

85 

-*-£ 

17. 

54 

-f- 

6. 

23. 

6. 

52 

-4. 

12. 

95 

-5. 

18. 

78 

•4- 

6. 

24. 

68  INTEGERS 

27.   Dividing  by  4,  5,  or  6 

19.  840-4. 
520  -  4. 

750  -*-  5. 
950  -  5. 
720  -  6. 
780  H-  6. 

25.  At  $4  each,  how  many  desks  can  be  bought  for  $48? 

26.  How  many  gallons  are  there  in  64  qt.  ? 

27.  At  $5  a  dozen,  how  many  dozen  baseballs  can  be 
bought  for  $65  ? 

28.  At  $6  a  head,  how  many  sheep  can  be  bought  for 
$126  ?    How  many  can  be  bought  for  $186  ? 

29.  How  many  inches  in  10  ft.?    How  many  times  does 
this  contain  4  in.  ?   How  many  times  does  it  contain  6  in.  ? 

28.   Dividing  by  7,  8,  or  9 

1.  70  -  7.  7.  72  -  8.  13.  54  -  9.  19.  840  -  7. 

2.  77-^7.  8.  56  —  8.  14.  81-9.  20.  980-7. 

3.  84-7.  9.  48-8.  15.  99-9.  21.  960 -=- 8. 

4.  63  -^  7.  10.  64  -  8.  16.  45  -  9.  22.  480  -  8. 

5.  91 -r- 7.  11.  88-^-8.  17.  72 -H  9.  23.  990  H-  9. 

6.  98  -f-  7.  12.  96  -r-  8.  18.  63  -=-  9.  24.  630  H-  9. 

25.  How  many  7's  are  there  in  49  ?    in  490  ?   in  497  ? 

26.  At  $7  a  dozen,  how  many  dozen  neckties  can  a  dealer 
buy  for  $84  ? 

27.  How  many  boards,  each  8  in.  wide,  will  cover  104  in. 
when  laid  side  by  side  ? 

28.  If  a  schoolroom  has  8  panes  of  glass  in  each  window, 
and  88  panes  in  all,  how  many  windows  are  there  ? 

29.  What  is  the  largest  number  of  baseball  nines  that 
can  be  formed  at  the  same  time  from  243  boys  ? 


DIVISION  69 

29.  Division 

1.  40  -  2.  7.  48  -f-  4.  13.  66  -<-  6.  19.  580  -  2. 

2.  48 -=-2.  8.  52-4.  14.  72-6.  20.  720-3. 

3.  58  -  2.  9.  56  -^  4.  15.  84  -  6.  21.  560  -  4. 

4.  60-3.  10.  35-7-5.  16.  64-4.  22.  850-5. 

5.  66  +  3.  11.  75  -  5.  17.  45  -  5.  23.  840  -f-  6. 

6.  72  —  3.  12.  85-5.  18.  90-6.  24.  540-6. 

25.  At  $6  each,  how  many  chairs  can  be  bought  for  $78  ? 

26.  At  5/  each,  how  many  pencils  can  I  buy  for  75/  ? 

27.  How  many  boxes,  each  5  in.  high,  in  a  pile  5  ft. 
high? 

28.  How  many  hands  (4  in.,  used  in  measuring  the  height 
of  horses)  in  72  in.  ? 

29.  If  I  wish  to  pay  $1.60  in  5-cent  pieces,  how  many 
do  I  need  ?    How  many  do  I  need  to  pay  $1.75  ? 

30.  Division 

1.42-7.  6.96-8.  11.96-3.  16.910-7. 

2.  56-7.  7.  54-9.  12.  96-4.  17.  960-8. 

3.  91  -  7.  8.  81  -  9.  13.  96  -  6.  18.  117  -  9. 

4.  48  -f-  8.  9.  99  -4-  9.  14.  98  -  7.  19.  900  -  5. 

5.  72-8.  10.  96-2.  15.  96-8.  20.  207-9. 

21.  How  many  pecks  in  64  qt.  ? 

22.  How  many  bushels  in  200  pk.  ? 

23.  How  many  yards  in  102  ft.  ? 

24.  How  many  gallons  in  200  qt.? 

25.  How  many  feet  in  240  in.  ? 

26.  At  $3  each,  how  many  hats  can  be  bought  for  $96  ? 

27.  At  $9  each,  how  many  desks  can  be  bought  for  $81  ? 

28.  At  $8  each,  how  many  rugs  can  be  bought  for  $104  ? 

29.  At  $7  a  dozen,  how  many  dozen  knives  can  be  bought 
for  $105  ? 


70  INTEGERS 

31.   Division 

We  may  say  that  21  -r-  2  =  10  with  remainder  1,  but  it  is  customary 
to  say  that  it  equals  10|. 


1.  21  -5-2. 

6.  32-3. 

11.  55-4. 

16.  89-5. 

2.  31  -s-  2. 

7.  52-3. 

12.  62-4. 

17.  37-6. 

3.  53  -=-2. 

8.  53  -  3. 

13.  36-5. 

18.  50  -r-  6. 

4.  75-2. 

9.  41-4. 

14.  47  -  5. 

19.  63  -  6. 

5.  31-3. 

10.  82-4. 

15.  68-5. 

20.  76-6. 

21.  By  what  number  must  2  be  multiplied  to  make  27  ? 

22.  What  number  must  be  multiplied  by  3  to  make  44  ? 

23.  By  what  number  must  75  be  divided  to  make  15  ? 

24.  If  $75  is  divided  equally  among  6  persons,  what  is 
the  share  of  each  ? 

25.  If  $101  is  divided  equally  among  4  persons,  what  is 
the  share  of  each  ? 

32.   Division 


1.  43  -  7. 

5.  49  -  8. 

9.  55-9. 

13.  77-6. 

2.  79-7. 

6.  50  -  8. 

10.  75-9. 

14.  67-7. 

3.  94-7. 

7.  67-8. 

11.  69-9. 

15.  57  -  8. 

4.  68  -=-  7. 

8.  76-8. 

12.  95  -v-  9. 

16.  47  -s-  9. 

17.  How  many  yards  in  46  ft.  ? 

18.  How  many  feet  in  24  in.  ?    in  30  in.  ? 

19.  How  many  gallons  in  100  qt.  ?    in  102  qt.  ? 

20.  How  many  gallons  in  32  pt.  ?    in  72  pt.  ?    in  74  pt.  ? 

21.  How  many  bushels  in  64  pk.  ?    in  70  pk.  ?   in  75  pk.? 

22.  If  8  boys  gather  76  qt.   of   nuts  and  divide  them 
equally,  what  is  the  share  of  each  ? 

23.  The  product  of  two  numbers  is  160  and  one  of  them 
is  8.    What  is  the  other  number  ? 

24.  The  product  of  two  numbers  is  164  and  one  of  them 
is  8.    What  is  the  other  number  ? 


DIVISION  71 

33.    Division  by  Multiples  of  10 


1.  220  H-  20. 
2.  960  -=-30. 
3.  640  H-  40. 
4.  850-5-50. 

5.  720  -=-60. 
6.  960  -f-  60. 
7.  560  -=-70. 
8.  910-*-  70. 

9.  640  -=-80. 
10.  1040  H-  80. 
11.  1170  H-  90. 
12.  1260  -r-  90. 

13.  How  many  minutes  in  540  sec.  ? 

14.  How  many  hours  in  420  min.  ? 

15.  By  what  number  must  30  be  multiplied  to  make  270  ? 

16.  By  what  number  must  we  multiply  40  to  make  320  ? 

17.  At  40  mi.  an  hour,  how  long  will  it  take  a  train  to 
go  280  mi.  ? 

18.  At  50  ini.  an  hour,  how  long  will  it  take  a  train  to 
go  250  mi.? 

19.  At  $80  a  head,  how  many  ponies  can  be  bought  for 
$960  ?    How  many  can  be  bought  for  $720  ? 

34.   Two-figure  Divisor 

1.  33  -=-  11.  5.  60  -=-  12.  9.  64  -=-  32. 

2.  77  -*-  11.  6.  72  -=-  12.  10.  96  -*-  32. 

3.  24  H-  12.  7.  32  -=-  16.  11.  480  --  16. 

4.  48  -=-  12.  8.  48  -v- 16.  12.  960  -=-  32. 

13.  How  many  feet  in  84  in.  ? 

14.  How  many  feet  in  60  in.  ?    in  66  in.  ?    in  63  in.  ? 

15.  How  many  quarts   in  1  bu.  ?     How    many   bushels 
in  64  qt.  ? 

16.  How  many  square  feet  in  1  sq.  yd.  ?   How  many 
square  yards  in  54  sq.  ft.  ? 

17.  How  many  ounces  in  a  pound  ?    How  many  pounds 
in  32  oz.  ?   in  320  oz.  ? 

18.  There  are  12  pence  in  an  English  shilling.   How  many 
shillings  are  there  in  132  pence  ? 

19.  How  many  feet  in  a  rod  ?    How  many  rods  in  33  ft.  ? 


72  INTEGERS 

35.   Review 


1.  28  +  28. 
2.  35  +  47. 
3.  29  +  27. 
4.  56  +  28. 

5.  72  -  35. 
6.  83  -  46. 
7.  84  -  37. 
8.  55-29. 

9.  2  x  36. 
10.  3  x  24. 
11.  4x37. 
12.  5  x  29. 

13.  56  -  2. 
14.  45-3. 
15.  72-4. 
16.  85  -=-  5. 

17.  What  is  the  cost  of  7  cows  at  $42  ? 

18.  What  is  the  cost  of  5  Ib.  of  meat  at  16/  ? 

19.  What  is  the  cost  of  2  bu.  of  wheat  at  85/  ? 

20.  What  is  the  cost  of  6  yd.  of  cotton  at  12/  ? 

21.  What  is  the  cost  of  3  Ib.  of  figs  at  18^  ? 

22.  What  is  the  length  of  4  boards,  each  14  ft.  long  ? 

23.  What  is  the  width  of  3  strips  of  cloth,  each  27  in. 
wide? 

24.  What  is  the  weight  of  5  bu.  of  corn,  each  bushel 
weighing  56  Ib.  ? 

36.   Review 


1. 

35  +  47. 

5. 

81- 

42. 

9. 

6x16. 

13. 

37  +  27. 

2. 

52- 

-36. 

6. 

5  x  17. 

10. 

72- 

6. 

14. 

80- 

-59. 

3. 

3x 

14. 

7. 

68- 

4. 

11. 

41  - 

28. 

15. 

7x 

12. 

4. 

72- 

-4. 

8. 

35  + 

29. 

12. 

65  + 

18. 

16. 

91- 

=-7. 

17.  What  is  a  quarter  of  the  sum  of  42  and  30  ? 

18.  If  7  sheep  cost  $56,  what  is  the  average  price  ? 

19.  If  5  Ib.  of  steak  cost  90/,  what  does  1  Ib.  cost  ? 

20.  If  2  yd.  of  cloth  cost  52/,  what  does  1  yd.  cost  ? 

21.  If  6  boys  weigh  306  Ib.,  what  is  the  average  weight  ? 

22.  What  is  an  eighth   of  the    difference   between  97 
and  25? 

23.  If  8  men  contribute  $96,  what  is  the  average  con- 
tribution ? 

24.  If  9  strips  of  ribbon  are  27  in.  wide,  what  is  the 
average  width  ? 


ADDITION  73 

II.    SHORT  METHODS 

37.   Addition 

In  short  columns  of  two-figure  numbers  add  both  columns  at  once. 
Thus,  in  Exercise  1,  think  22,  32,  35,  45,  50,  stating  only  the  answer. 

1.  15  4.  20  7.  20  10.  15  13.  15 

13  16  25  27  44 

22  34  35  38  36 


2. 

23 

5.  27 

8.  49 

11.  62 

14.  34 

54 

28 

32 

31 

26 

36 

29 

36 

43 

31 

3. 

22 

6.  42 

9.  21 

12.  48 

15.  27 

32 

23 

32 

22 

13 

44 

35 

41 

27 

26 

38.   Addition 


1.  52 

3.  45 

5.  $2.62 

7.  $2.50 

9.  $1.20 

64 

38 

3. 

1.80 

2.60 

48 

22 

4.80 

1.20 

2.40 

2.  24 

4.  25 

6.  $1.50 

8.  $3.75 

10.  $3.35 

36\ 

32 

.25 

1.20 

2.25 

80  \ 

33 

2.75 

1.80 

2.75 

11.  Add  1  +  2  +  3  +  4  +  5  +  6. 

12.  My  purchases  cost  37^,  42^,  and  50/.    What  is  the 
total ? 

13.  Three  boys  weigh  68  lb.,  72  lb.,  64  Ib.    What  is  their 
total  weight  ? 

14.  If  I  pay  $2.50  for  a  hat,  $3  for  some  shoes,  and 
$6.50  for  a  coat,  what  do  all  three  cost  ? 


74  SHORT  METHODS 

39.  Subtraction 

There  are  two  short  methods  of  subtracting  217  from  900.  We  may 
think  of  900  as  800  +  90  +  10,  and  subtract  from  left  to  right,  8-2 
=  6,  9  —  1  =  8,  10  —  7  =  3,  thus  easily  reading  the  result,  683.  Or  we 
may  "make  change,"  thus,  217  +  3  =  220,  220  +  80  =  300,  300  + 
600  =  900  ;  therefore  the  result  is  683. 

Subtract  by  the  first  of  these  methods  : 

1.  600  -  73.  6.  400  -  142.  11.  $7  -  $1.64. 

2.  700  -  82.  7.  $9  -  $1.35.  12.  $9  -  $2.88. 

3.  500  -  67.  8.  $8  -  $2.65.  13.  $10  -  $1.25. 

4.  800  -  128.  9.  $7  -  $4.28.  14.  $10  -  $2.73. 

5.  600  -  237.  10.  $8  -  $2.27.  15.  $10  -  $5.26. 

16.  Subtract  $26.50  from  $100. 

17.  If  my  purchases  amount  to  $7.28,  how  much  change 
should  I  receive  from  $10  ? 

40.  Subtraction 

Subtract  by  the  "  making  change  "  method : 

1.  $5 -$2.75.  5.  $10 -$7.20.  9.  $15  -  $13.20. 

2.  $5 -$3.20.  6.  $10 -$1.75.  10.  $20  -  $11.25. 

3.  $5 -$1.80.  7.  $15 -$10.75.  11.  $20  -  $16.40. 

4.  $10  -  $6.25.  8.  $15  -  $12.30.  12.  $20  -  $18.30. 

13.  If  my  purchases  amount  to  $2.50  and  $1.25,  how 
much  change  should  I  receive  from  $5  ? 

14.  If  I  buy  8  yd.  of  cloth  at  30/  a  yard,  how  much 
change  should  I  receive  from  $5  ? 

15.  If  I  buy  I  yd.  of  velvet  at  $1.60  a  yard,  how  much 
change  should  I  receive  from  $1? 

16.  If  I  buy  21  yd.  of  cloth  at  50/  a  yard,  how  much 
change  should  I  receive  from  $15  ? 

17.  If  I  buy  1J  yd.  of  silk  at  $1.50  a  yard,  how  much 
change  should  I  receive  from  $5  ? 


SUBTRACTION  75 

41.  Review 

Find  the  total  cost  in  each  example  : 

1.  4  Ib.  of  figs  at  18/  a  pound. 

2.  8  Ib.  of  rice  at  12/  a  pound. 

3.  8  cans  of  tomatoes  at  15/  a  can. 

4.  36/  worth  of  cheese,  and  3  doz.  eggs  at  30/  a  dozen. 

5.  18/  worth  of  spice,  22/  worth  of  raisins,  and  60/ 
worth  of  tea. 

6.  3  bottles  of  olives  at  20/  each,  and  2  bottles  of  pickles 
at  15/  each. 

7.  10  Ib.  of  sugar  at  8/  a  pound,  and  a  15/  can  of 
mustard. 

8.  Half  a  dozen  boxes  of  crackers  at  10/  a  box,  and  2 
boxes  of  tea  at  40/  a  box. 

Find  the  change  due  in  each  example : 

9.  2  Ib.  of  butter  at  32/  a  pound  ;  $1  paid. 

10.  6  cans  of  soup  at  15/  a  can ;  $1  paid. 

11.  15/  worth  of  allspice,  and  2  cans  of  peaches  at  22/ 
each ;  $1  paid. 

12.  10  Ib.  of  oatmeal  at  6/  a  pound,  and  6  cans  of  plums 
at  20/  each ;  $5  paid. 

13.  A  30/  box  of  pepper,  28/  worth  of  codfish,  and  2 
boxes  of  cereal  at  20/  a  box ;  $5  paid. 

14.  $2.60  worth  of  canned  goods,  20  Ib.  of  sugar  at  7/  a 
pound,  and  $2.25  worth  of  vegetables ;  $10  paid. 

15.  20  yd.  of  cloth  at  50  /  a  yard  and  10  yd.  of  lining  at 
30/  a  yard  ;  $15  paid. 

16.  A  5-cent  bottle  of  mucilage,  10/  worth  of  ink,  75/ 
worth  of  stationery,  and  a  book  costing  $1.20 ;  $5  paid. 

17.  An  arithmetic  costing  45/,  a  writing  tablet  costing* 
8/,  3  pencils  at  4/  each,  and  5/  worth  of  pens ;  $1  paid. 


76  SHORT  METHODS 

42.  Multiplication 

Multiply  by  10  by  the  shortest  method  you  know : 
1.  77.  2.  82.         3.  $6.40.       4.  $.34.  5.  $1.27. 

Multiply  by  100  : 
6.  83.  7.  43.         8.  $.72.         9.  $.63.         10.  $2.46. 

Multiply  by  1000  : 
11.  29.  12.  68.       13.  $.32.       14.  $1.27.       15.  $3.48. 

Multiply  by  5  by  the  shortest  method  you  knoiv  : 
16.  28.  17.  34.       18.  $.40.       19.  $2.48.       20.  $4.04. 

Multiply  by  25  : 
21.  24.          22.  48.       23.  $.80.       24.  $2.44.       25.  $8.04. 

43.  Multiplication 

Multiply  by  33\  by  multiplying  by  100  and  dividing  by  3: 
1.  6.  2.  75.         3.  48.  4.  $.24.  5.  $1.23. 

Multiply  by  12 j  : 
6.  8.  7.  48.         8.  24.  9.  $.64.         10.  $8.40. 

Multiply  by  9  by  subtracting  the  number  from  10  times  itself: 
11.  12.  12.  32.        13.  16.          14.'  45.  15.  35. 

Multiply  by  11  by  adding  the  number  to  10  times  itself : 
16.  12.  17.  32.        18.  41.          19.  52.  20.  71. 

Multiply  by  125  by  multiplying  by  1000  and  dividing  by  8  : 
21.  32.          22.  24.       23.  88.          24.  $2.48.       25.  $8.16. 


MULTIPLICATION  77 

44.   Multiplication 

Find  the  cost  of  the  following  : 

1.  10  yd.  of  linen  at  87/. 

2.  10  Ib.  of  feathers  at  46/. 

3.  10  yd.  of  burlap  at  $1.15. 

4.  10  gross  of  buttons  at 

5.  100  yd.  of  carpet  at 

6.  100  yd.  of  canvas  at  53/. 

7.  100  yd.  of  cheese  cloth  at 

8.  100  feather  boxes  at  37£/. 

9.  1000  yd.  of  jute  burlap  at 

10.  1000  yd.  of  toweling  at 

11.  5  yd.  of  cotton  cloth  at  24/. 

12.  5  yd.  of  farmer's  satin  at  42/. 

13.  5  doz.  whalebones  at  $2.38  a  dozen. 

14.  5  balls  of  fine  cotton  at  36/. 

15.  25  yd.  of  felt  at  $1.64. 

16.  25  yd.  of  cambric  at  12/. 

17.  25  yd.  of  coarse  linen  at  48/. 

18.  25  yd.  of  fine  Persian  lawn  at  32/. 

19.  125  yd.  of  linoleum  at  80/. 

20.  125  yd.  of  Brussels  carpet  at  $1.20. 

21.  125  yd.  of  ingrain  carpet  at  64 /. 

22.  125  Ib.  of  hammock  cord  at  24/. 

23.  24  yd.  of  common  Persian  lawn  at  250, 

24.  24  yd.  of  Axminster  carpet  at  $1.25. 

25.  72  yd.  of  toweling  at 

26.  64  yd.  of  cambric  at 

27.  25  yd.  of  Brussels  carpet  at  $1.60. 

28.  28  acres  of  meadow  land  at  $80. 

29.  125  acres  of  pasture  land  at  $64. 

30.  50  cords  of  wood  at  $3 ;  at  $3.60. 


78  SHORT  METHODS 

45.   Multiplication 
Find  the  cost  of  the  following  : 
1.  60  Ib.  of  fine  candy  at 


2.  900  Ib.  of  tea  at 

3.  16  doz.  eggs  at 

4.  96  cans  of  plums  at 

5.  12£  Ib.  of  butter  at  24/. 

6.  30  cases  of  lemon  soda  at 

7.  12  Ib.  of  licorice  drops  at  3  Ib.  for  $1. 

8.  80  Ib.  of  peanut  brittle  at  12£/. 

9.  9  Ib.  of  mixed  candy  at  25/. 

10.  9  boxes  of  caramels  at  $1.20. 

11.  9  boxes  of  chocolate  almonds  at  $1.30. 

12.  9  boxes  of  pepsin  gum  at  60/. 

13.  11  doz.  boxes  of  chocolates  at  $1.80  a  dozen. 

14.  11  boxes  of  salted  peanuts  at  80/. 

15.  11  boxes  of  vanilla  chocolates  at  75/. 

16.  11  Ib.  of  fine  chocolate  creams  at  52/. 

17.  If  a  grocer  buys  600  Ib.  of  tea  and  sells  it  at  a  profit 
of  ll/  a  pound,  how  much  does  he  gain  ? 

18.  If  a  grocer  buys  200  doz.  cans  of  soup  and  sells  it 
at  a  profit  of  25/  a  dozen,  how  much  does  he  gain  ? 

19.  If  a  grocer  buys  80  bbl.  of  sugar  and  sells  it  at  a 
profit  of  $1.25  a  barrel,  how  much  does  he  gain  ? 

20.  If  a  dry  goods  dealer  buys  640  yd.  of  silk  and  sells  it 
at  a  profit  of  25/  a  yard,  how  much  does  he  gain  ? 

21.  If  a  carpet  dealer  buys  810  yd.  of  carpet  and  sells  it 
at  a  profit  of  9/  a  yard,  how  much  does  he  gain  ? 

22.  If  a  bookseller  sells  220  arithmetics  and  makes  a 
profit  of  7/  on  each,  how  much  is  his  total  profit  ? 

23.  If  a  creamery  sells  720  Ib.  of  butter  at  25/  a  pound, 
how  much  does  it  receive  for  all  the  butter  ? 


DIVISION  79 

46.  Division 

Divide  by  10  by  the  shortest  method  you  know : 

1.  70.          3.  750.        5.  800.        7.  160.  9.  1250. 

2.  60.          4.  820.        6.  600.        8.  320.          10.  6250. 

Divide  by  100  : 

11.  700.      12.  800.      13.  7500.    14.  40,000.    15.  7000. 

Divide  by  1000  : 

16.  6000.    17.  5000.    18.  2000.    19.  35,000.    20.  62,000. 

Divide  by  5  by  dividing  by  10  and  multiplying  by  2 : 

21.  120.        24.  640.        27.  220.        30.  810.        33.  650. 

22.  600.        25.  360.        28.  640.        31.  800.        34.  540. 

23.  160.        26.  720.        29.  420.        32.  710.        35.  260. 

47.  Division 

Divide  by  25  by  dividing  by  100  and  multiplying  by  4  •' 
1.  500.         2.  600.         3.  800.        4.  1200.       5.  2200. 

Divide  by  125  by  dividing  by  1000  and  multiplying  by  8  : 
6.  5000.       7.  6000.       8.  8000.      9.  1500.     10.  12,000. 

Divide  by  12^  by  dividing  by  100  and  multiplying  by  8  : 
11.  200.        12.  300.       13.  700.      14.  75.         15.  150. 

Divide  by  33^  by  dividing  by  100  and  multiplying  by  3 : 
16.  200.       17.  500.       18.  800.      19.  333£.     20.  300. 

Perform  these  divisions  : 

21.  1230 --5.  22.  2150-5-25.  23.  1000 -j- 125. 


80  SHORT  METHODS 

48.   Division 

£>l.  If  10  yd.  of  gingham  cost  $1.20,  what  does  1  yd.  cost  ? 
(/2.  If  10  doz.  buttons  cost  $1.30,  what  does  1  doz.  cost? 
13.  If  10  yd.  of  chambray  cost  $2.20,  what  does  1  yd. 
cost? 

4.  If  10  yd.  of  velvet  carpet  cost  $13.50,  what  does 
1  yd.  cost  ? 

5.  If  100  yd.  of  Brussels  carpet  cost  $84,  what  does 
1  yd.  cost  ? 

6.  If  100  yd.  of  oilcloth  cost  $37.50,  what  does  1  yd. 
cost? 

7.  If  100  gross  of  bone  buttons  cost  $22.50,  what  does 
1  gross  cost  ? 

8.  If  100  pieces  of  binding  cost  $12.50,  what  does  1 
piece  cost? 

9.  If  1000  yd.  of  canvas  cost  $450,  what  does  1  yd.  cost? 

10.  If  1000  yd.  of  dimity  cost  $140,  what  does  1  yd.  cost? 

11.  If  1000  yd.  of  ingrain  carpet  cost  $520,  what  does 
1  yd.  cost  ? 

12.  If  1000  pieces  of  braid  cost  $85,  what  does  1  piece 
cost? 

13.  If  5  yd.  of  cotton  flannel  cost  80/,  what  does  1  yd. 
cost? 

14.  If  5  yd.  of  linen  cost  $2.40,  what  does  1  yd.  cost  ? 

15.  If  5  yd.  of  crinoline  cost  55/,  what  does  1  yd.  cost  ? 

16.  If  5  balls  of  crochet  cotton  cost  $2.40,  what  does  1 
ball  cost  ? 

17.  If  25  yd.  of  cashmere  cost  $20,  what  does  1  yd.  cost  ? 

18.  If  125yd.  of  carpet  cost  $100,  what  does  1  yd.  cost? 

19.  If  12^  doz.  boxes  cost  $30,  what  does  1  doz.  cost  ? 

20.  If  33£  yd.  of  cloth  cost  $9,  what  does  1  yd.  cost  ? 

21.  If  33^  yd.  of  oilcloth  cost  $12,  what  does  1  yd.  cost  ? 

22.  If  125  cows  cost  $5000,  what  does  1  cow  cost  ? 


REVIEW  81 

49.   Review 

vi.  If  a  man  earns  $2.40  a  day  for  10  da.,  and  $2.50  a 
day  for  2  da.,  how  much  does  he  earn  in  the  12  days  ? 

2.  If  a  merchant  buys  goods  for  $120,  $70,  $60,  and 
$100,  and  sells  them  for  $450,  how  much  does  he  gain  ? 

3.  If  a  man  carts  away  75  loads  of  dirt  at  33^/  a  load, 
how  much  should  he  receive  ? 

4.  If  a  plasterer  does  some  work  at  12^/  a  square  yard, 
how  much  should  he  receive  for  160  sq.  yd.  ? 

5.  If  a  farmer  sells  11  doz.  eggs  to  a  grocer  at  16/  a 
dozen,  and  buys  75/  worth  of  sugar,  what  balance  is  due? 

i/6".  If  a  vegetable  gardener  set  out  320  tomato  plants, 
but  lost  -J  of  them  by  frost,  how  many  had  he  left  ? 

7.  Suppose  you  go  to  a  grocery  and  make  purchases 
amounting  to  $1.20,  GO/,  35/,  and  15/.  How  much  change 
should  you  receive  from  $2.50  ? 

*4f.  Suppose  a  boy  buys  6  fishing  flies  at  10/,  a  rod  at 
$1.25,  and  pays  30/  for  a  line.  How  much  change  should 
he  receive  from  $2.25?. 

9.  If  a  man's  income  is  $1200  a  year  and  his  expenses 
are  $825,  how  much  does  he  save?'' 

10.  If  a  boy  earns  72/  one  week  and  84/  the  next,  and 
then  puts  $1.50  in  the  savings  bank,  how  much  has  he  left  ? 

11.  If  you  walk  160  yd.  away  from  the  schoolhouse  and 
75  yd.  back,  how  far  are  you  then  from  the  schoolhouse  ? 

12.  If  you  walk  225  yd.  directly. north  from  here  and  then 
turn  and  walk  300  yd.  south,  how  far  will  you  then  be  from 
here  and  in  what  direction  ? 

1^13.  If  a  man  is  in  debt  $750  and  pays  $370  on  the  debt, 
how  much  does  he  still  owe  ? 

14.  If  a  man  is  in  debt  $275  at  the  beginning  of  a  year 
and  saves  $600  that  year,  how  much  will  he  have  after 
paying  the  debt? 


82  COMMON  FRACTIONS 

III.    COMMON  FRACTIONS 

50.   Factors 

The  prime  factors  of  36  are  2,  2,  3,  3.    Numbers  like  7,  11,  17,  and 
23  are  themselves  prime  and  have  no  factors. 

Find  the  prime  factors  in : 

1.  6.          4.  33.  7.  51.  10.  64.  13.  77. 

2.  9.          5.  34.          8.  88.  11.  75.  14.  49. 

3.  21.        6.  35.          9.  72.  12.  65.  15.  91. 

Find  only  one  prime  factor  in: 

16.  707.  21.  108.  26.  147.  31.  220.  36.  243. 

17.  330.  22.  145.  27.  312.  32.  121.  37.  705. 

18.  135.  23.  213.  28.  321.  33.  130.  38.  603. 

19.  712.  24.  635.  29. -123.  34.  143.  39.  357. 

20.  414.  25.  637.  30.  111.  35.  707.  40.  497. 

51.   Multiples 

Two  multiples  of  3  are  6  and  9,  or  9  and  12,  and  so  on.   Any  num- 
ber has  an  indefinitely  large  number  of  multiples. 

Find  any  two  multiples  of: 

1.  2.  3.  7.  5.  11.  7.  14.  9.  31. 

2.  5.          4.  9.  6.  13.  8.  23.  10.  70. 

The  number  54  is  a  multiple  common  to  both  6  and  9,  but  18  is  the 
least  multiple  that  is  common  to  both  6  and  9. 

Find  any  multiple  common  to  these  two  numbers : 

11.  2,  5.  12.  4,  10.  13.  7,  11.  14.  8,  12. 

The  number  18  is  the  least  common  multiple  of  6  and  9  ;  9  is  the 
least  common  multiple  of  3  and  9. 

Find  the  least  common  multiple  of  these  two  numbers : 
15.  2,  4.  '         16.  3,  8.  17.  6,  8.  18.  8,  12. 


Reduce  as  indicated 

REDUCTION 
52.   Reduction 

83 

To  halves  : 

1. 

t- 

2. 

TV 

3. 

1- 

4. 

if- 

To 

fourths  : 

5. 

1- 

6. 

1- 

7. 

TV 

8. 

TV 

To 

fifths  : 

9. 

TV 

10. 

TV 

11. 

M- 

12. 

tU- 

To 

sixths  : 

13. 

§• 

14. 

£ 

15. 

8 

16. 

6m 

To 

eighths  : 

17. 

i 

18. 

4- 

19. 

if- 

20. 

H- 

To 

twelfths  : 

21. 

1 

22. 

¥' 

23. 

|. 

24. 

f 

To 

sixteenths  : 

25. 

i- 

26. 

4- 

27. 

1- 

28. 

3-V 

To 

thirty-seconds  : 

29. 

i- 

30. 

1 

4" 

31. 

3 
4- 

32. 

5 

"8"' 

To 

forty-eighths  : 

33. 

*• 

34. 

i« 

35. 

I- 

36. 

%. 

To 

ninths  : 

37. 

i- 

38. 

f- 

39. 

t- 

40. 

it- 

To 

fifteenths  : 

41. 

i- 

42. 

I- 

43. 

I- 

44. 

f- 

To 

twentieths  : 

45. 

i- 

46. 

3_ 

47. 

f. 

48. 

a. 

To 

twenty  -fourths  : 

49. 

3 

4- 

50. 

2_ 

51. 

f 

52. 

3 

'8"- 

53. 

Reduction 

Reduce  as  indicated  : 

To 

halves  : 

1. 

f- 

2. 

f- 

3. 

A" 

4. 

A 

4" 

To 

thirds  : 

5. 

t- 

6. 

8_ 

7. 

t- 

8. 

8 

To 

fourths  : 

9. 

3 
2- 

10. 

I 

11. 

4 

"8"' 

12. 

ft' 

To 

fifths  : 

13. 

TV 

14. 

3 

15. 

M- 

16. 

H- 

To 

sixths  : 

17. 

3"' 

18. 

TV 

19. 

r\- 

20. 

I- 

To 

sevenths  : 

21. 

TV 

22. 

if- 

23. 

M- 

24. 

30.. 

To 

eighths  : 

25. 

it- 

26. 

1- 

27. 

T\- 

28. 

f£. 

To 

ninths  : 

29. 

3~- 

30. 

1- 

31. 

TV 

32. 

§5- 

To 

twelfths  : 

33. 

f. 

34. 

I- 

35. 

|. 

36. 

ft' 

To 

sixteenths  : 

37. 

7 

38. 

3 
4' 

39. 

1- 

40. 

It- 

To 

eighteenths  : 

41. 

5- 

42. 

|. 

43. 

5^ 

44. 

f 

To 

twenty-fourths: 

45. 

|. 

46. 

!• 

47. 

5 

48. 

t- 

To 

thirty-seconds  : 

49. 

3 

50. 

1- 

51. 

TV 

52. 

if 

84  COMMON  FRACTIONS 

54.   Integers  to  Fractions 

8  7  x  8         56 

Since  1  =  - ,  therefore   7  = or  —    In  the  same  way  we 

8  88 

may  reduce  any  integer  to  a  fractional  form. 
Reduce  as  indicated: 


To 

halves  : 

1. 

1. 

2. 

3. 

3. 

7. 

4. 

15. 

To 

thirds  : 

5. 

1. 

6. 

5. 

7. 

8. 

8. 

12. 

To 

fourths  : 

9. 

2. 

10. 

6. 

11. 

7. 

12. 

10. 

To 

fifths  : 

13. 

3. 

14. 

5. 

15. 

9. 

16. 

12. 

To 

sixths  : 

17. 

4. 

18. 

6. 

19. 

8. 

20. 

11. 

To 
To 

eighths  : 
twelfths  : 

21. 
25. 

3. 
2. 

22. 
26. 

8. 
3. 

23. 

27. 

9. 
4. 

24. 
28. 

12. 
10. 

To 

sixteenths  : 

29. 

2. 

30. 

3. 

31. 

4. 

32. 

10. 

To 
To 

thirty-seconds  : 
fifteenths  : 

33. 
37. 

1. 
1. 

34. 
38. 

2. 
2. 

35. 
39. 

3. 
3. 

36. 
40. 

10. 
5. 

55.   Reduction 

Since  1  =  |,  therefore  \\  =  f  +  |,  or  f.    In  the  same  way  we  may 
reduce  any  mixed  number  to  an  improper  fraction. 

Reduce  to  improper  fractions : 

1.  1£.  6.  2TV  11.  13V  16.  1?V 

2.  2J.  7.  2ft.  12.  13V  17.  1?V 

3.  2|.  8.  2^.  13.  23V  18.  1ft. 

4.  3f.  9.  1TV  14.  2&.  19.  25V 

5.  2f.  10.  2TV  15.  2&.  20.  3T^. 

21.  Express  6f  as  thirds.    In  6|  yd.  how  many  feet? 

22.  Express  Sy7^  as  twelfths.  In  5T\  ft.  how  many  inches  ? 

23.  Express  10^  as  twelfths.    In  10/j  yr.  how  many 
months,  calling  ^  yr.  exactly  1  mo.  ? 

24.  Express  3^  as  thirtieths.   In  3^  mo.,  how  many  days, 
calling  30  da.  exactly  1  mo.  ? 


REDUCTION  85 

56.   Reduction 

Reduce  to  integers : 


1.  f.  4.   V-.  7.  -V-.  10.  \V-          13-  ft- 

2.  f.     ^       5.  -V2.  8-  ^i3-'          11-  -W-          14-  ||. 

3.  .L6..    /'     e.  -87*.  9.  -2TV--          12.  \2/.          15.  -V^0. 


Reduce  to  mixed  numbers : 

•     19'    *^'  '^.  j*2*",,"*''  f     i*    *y/x^r'/r         *°*    t*'^ 


16.  K>  i  19-  ¥-'^f-*2/.  -v--7i  25-  -v-     #*•  *£•-' 

17.  -y-  5  £  20.  y.  ff%tit$*$.  <{  %,  26^4f  ^  29. 


18.  V.:.    '    21.  -y-.ll^  24.  ^.  ,         27.  M.  ,         30. 


'-.-•^    CTSw-       £  • 

k/'filjv- 

79A       76  , 

^  -^^         ^"'  ""'    T5^ 

Reduce  to  integers  or  mixed  numbers :   " 

31.  V-          34-    ff          37-  W-          40-  fi-  43. 

32.  |f.         35.  -^.         38.  J^0--         41.  i^a.         44. 

33.  -V-.          36.  ff.          39.  f§.  42.  ^^.          45. 

57.  Reduction 

Reduce  to  lowest  terms : 

I-  I-  V       5-  A-   i        9-  M-  13-  if-  17. 

2.  f.    2,-      6.  ||.§     10.  J|.  14.  if.  18.  ,5ft. 

3-  iI-3        7.  H.£H.  A-  15-  II-  19-  T%V 

420    r^y     a      e  19     in  ic      15  on      75 

•  Tff-  i  jE,    °-  55-          i4-   4^5-  1D-   TOO"-          •*"•   TTJO- 

21.  On  a  ^railway  time  table  the  distance  between  two 
stations  is  given  as  46^%  mi.   Express  this  in  lower  terms. 

22.  A  ruler  is  marked  in  thirty-seconds  of  an  inch.    A 
piece  of  veneer  is  measured  and  found  to  be  -fc  in.  thick. 
Express  this  thickness  in  lower  terms. 

23.  A  surveyor  uses  a  chain  66  ft.  long,  made  of  100 
links.    He  measures  a  certain  distance  and  finds  it  to  be 
1  chain  and  50  links.    Express  this  as  a  chain  and  a  frac- 
tion :  as  feet. 


86  COMMON  FRACTIONS 

58.  Addition 

We  add  fractions  having  the  same  denominator  as  follows  : 

T\  +  T3S=T8S  =  £-     AlSO,   f  +  f  =  f=lf 

1.  £  +  §•  >  7.  i  +  f.           13.  ^  +  T&.  //  19-  5  +  |. 

2.  *  +  f .  /  8.  TV  +  TV    -,14.  ^  +  ft.    '  20.  ||  +  A, 

3.  f  +  f  '  9.  T<V  +  TV  >15.  ^  +  if-       21.  H  +  3f 
*•*  +  *•  ',  10-  iV  +  TV  £16.  A  +  A-       22-  H  +  2|. 

5.  i  +  \M  11.  TV  +  A-^/ 17.  |  +  f  23.  2|  +  If 

6.  i  +  |.  ^12.  TV  +  \\.,     18.  |  +  |.  24.  3f  +  1|. 

25.  Add  \,  %$,  and  f 

26.  The  three  sides  of  a  triangle  are  l£  in.,  1|  in.,  and 
1|  in.    What  is  the  perimeter  ? 

27.  How  much  picture  molding  is  needed  for  a  frame 
5|  in.  long  and  3£  in.  wide  ? 

59.  Addition 

'Think  of  f  +  f  as  f  +  f ,  or  ^\  or  If.    Proceed  in  the  same  way 
with  other  fractions  having  different  denominators. 

1.  i  +  f  6.  i  +  |.  11.  |  +  |.  16.  *  +  |. 

2.  i  +  |.  7.  i  +  f  12.  |  +  |.  17.  H  +  2J. 

3.  i  +  f  8.  i  +  |.  13.  J  +  f  18.  3|  +  If 

4.  i  +  f  9.  i  +  |.  14.  J  +  f .  19.  24  +  3f 

5.  i  +  f  10.  i  +  f  15.  i  +  f  20.  3J  +  If 

21.  How  much  is  $5^  and  $6|  ? 

22.  How  much  is  $10f  $5f  and  $4^  ? 

23.  If  I  buy  $10f  worth  of  coal  and  $7£  worth  of  wood, 
how  much  is  my  total  bill  ? 

24.  What  is  the  number  from  which  if  2  is  taken  the 
result  is  1  ?   from  which  if  2^  is  taken  the  result  is  l£  ? 

25.  What  number  must  be  added  to  3^  ft.  to  make  4  ft.  ? 
to  make  4    ft.  ? 


ADDITION  AND  SUBTRACTION  87 

60.   Addition 

I-   *  +  f  5.  i  +  TV-  9.   £  +  TV  13.  i  +  Jr 

2.   i  +  f  6.  i  +  A-  10.   |  +  TV  14.  i  +  &. 

3-  f  +  i.  7.  i  +  TV  11.  f  +  T3,.  15.  i  +  ^ 

4.  f  +  f .  8.  f  +  ^.  12.   |  +  A.  16.  I  +  A. 

17.  The   three   sides  of  a  triangle   are    1^  in.,  1T^  in., 
1^  in.    What  is  the  perimeter  ? 

18.  A  field  is  20  rd.,  24  rd.,  25J  rd.,  and  21|  rd.  on  the 
four  sides.    What  is  the  perimeter  ? 

19.  Four  packages  weigh  12£  lb.,  13*   lb.,  10|  lb.,  and 
lOf  lb.   What  is  the  total  weight  ? 

20.  The  page  of  a  book  is  4f  in.  wide  and  7T^  in.  long. 
What  is  the  sum  of  the  two  sides  ?    What  is  the  perimeter  ? 

21.  A  picture  is  3^  in.  wide  and  the  mat  is  1^  in.  wide 
on  each  side.    How  wide  is  the  picture  and  mat  together  ? 

61.    Subtraction 

We  subtract  fractions  having  the  same  denominator  as  follows : 
A  -  A  *  T25  =  f    Also  3J  -  1  =  2|  -  1  =  2|  =  2J. 

1-  f  -  i-          6.   f  -  |.       11.  TV  -  TV       16.  If  -  f . 

2-  I  ~  I-          M  -  *'       12'  "  -  A-      17'  2*  -  *• 

3-  I  -  f  •          8.  |  -  f .       13.  TV  -  TV      18.  3|  -  |. 

1  f  -4         9.  f  -  f       14.  A  -  A-      19-  3A  -  1^. 

5.  |  -  f .        10.  f  -  f       15.   1 1  -  ^.      20.  4i|  -  2^. 

21.  If  I  have  $5|  and  spend  $li,  how  much  have  I  left  ? 

22.  If  I  have  $5^  and  spend  $f ,  how  much  have  I  left  ? 

23.  If  I  have  $5i  and  spend  $2|,  how  much  have  I  left  ? 

24.  What  must  be  added  to  6|  bu.  to  make  5|  bu.  ? 

25.  What  must  be  added  to  3|  in.  to  make  51  in.? 

O  o 

26.  What  must  be  added  to  10|  rd.  to  make  15i  rd.? 

27.  How  much  longer  is    llj3^   in.  than  5|   in.?    than 
3f  in.? 


88 


62.   Different  Denominators 

We  subtract  \  from  f  thus  :  J  —  £  =  f  —  f  =  £. 

-^  11.     - 


2- 
3- 
4- 

5. 


7.  i  -  ^. 

8.  §-Tj. 

9.  f  -  |. 


13.        - 


is.  2^-f 

d  17.  2f  -  |. 
^18.  3§-£. 
19.  3H  -  f 

20-  4*  -  ^* 

in.    How  thick 


21.  A  boafS/L  in.  thick  is  'planed  down 
is  it  then  ? 

22.  A  board  £  in.  thick  is  planed  down  ^  in.    How  thick 
is  it  then  ? 

23.  If  I  have  $2$  and  spend  $J,  how  much  have  I  left? 
How  much  shall  I  have  left  if  I  spend  $^  more? 

24.  From  a  strip  of  wood  7|  in.  long  a  length  of  f  in. 
is  cut.    How  long  is  the  strip  then  ? 


63.   Subtraction  of  Fractions 


1. 

2. 
3. 

4. 


-TV 


5. 
6. 
7. 

8. 


9. 
10. 
11. 
12. 


13. 
14. 
15. 
16. 


03    _ 

^4 


17.  A  plank  1|  in.  thick  is  planed  down 
thick  is  it  then  ? 

18.  From  a  piece    of   picture  molding  7  ft. 


-T1; 


n. 


-2f 

How 

long 


there  is  cut  a  piece  2  ft.  l£  in.  long.    How  long  is   the 
remainder  ? 

19.  A  piece  of  marble  83\  in.  thick  is  polished  down  ^ 
in.  "What  is  then  the  thickness  ?    How  much  more  will  it 
have  to  be  polished  down  to  be  exactly  8  in.  thick  ? 

20.  A  piece  of  cloth  7£  in.  wide  is  folded  so  as  to  be  f  in. 
less  in  width.    How  wide  is  it  then  ?   How  much  more  will 
have  to  be  folded  in  to  have  it  6    in.  wide  ? 


7. 

i 

4 

of 

48. 

13. 

1 

of 

48. 

19. 

f  of. 

60. 

8. 

3 
f 

of 

48. 

14. 

•& 

of 

40. 

20. 

i  of 

66. 

9. 

3 

of 

88. 

15. 

^ 

of 

39. 

21. 

I  of 

60. 

10. 

I 

of 

64. 

16. 

2 
^ 

of 

27. 

22. 

4  of 

25. 

11. 

I 

of 

64. 

17. 

1 

of 

75. 

23. 

i  of 

22. 

12. 

of 

36. 

18. 

A 

of 

48. 

24. 

^of 

33. 

MULTIPLICATION  89 

64.  Multiplication  by  a  Fraction 

1.  ^of20. 

2.  i  of  28. 

3.  i  of  50. 

4.  ^of  58. 

5.  4  of  32. 

6.  fc  of  21. 

25.  How  much  is  half  the  sum  of  27  and  37  ? 

26.  If  the  perimeter  of  an  equilateral  (equal-sided)  tri- 
angle is  51  in.,  what  is  the  length  of  each  side  ? 

27.  If  the  perimeter  of  a  square  is  52  in.,  what  is  the 
length  of  each  side  ? 

28.  If  a  man  has  480  acres  of  land,  and  ^  is  wooded,  how 
many  acres  are  wooded  ?    If  f  is  meadow  land,  how  many 
acres  are  meadow  land  ? 

65.  Multiplication  by  an  Integer 

16.  2xf. 

17.  2  x  TV 

18.  6  x  TV 

19.  3  x  fV 

20.  6  x  TV 

21.  If  each  side  of  a  triangle  is  f  in.,  what  is  the  perimeter? 

22.  If  one  side  of  a  square  is  f  in.,  what  is  the  perimeter? 

23.  At  $4  a  dozen,  how  much  will  6  doz.  eggs  cost  ?  8  doz.  ? 

24.  At  $4  a  yard,  how  much  will  9  yd.  of  cloth  cost  ? 

25.  If  you  live  f  mi.  from  school,  and  I  live  twice  as  far 
away,  how  far  from  school  do  I  live  ? 

26.  If  a  board  is  £  in.  thick,  how  thick  will  be  a  pile  of 
32  such  boards  ? 

27.  If  each  boy  can  pull  ^  of  a  ton,  what  fraction  of  a 
ton  can  8  boys  pull  ? 


1         ^   N/    1 

6.  8  x  f  . 

11.   8x  I. 

2.  4x1-. 

7.  6  x  f  . 

12.  16  xl 

3.  4  x  i- 

8.  12  x  a. 

13.  6  x  ^. 

4.  4  x  TV 

9.  4  x  f  . 

14.  6x§. 

5.  4  x  |. 

10.  8xf 

15.  5x§. 

90  COMMON  FRACTIONS 

66.  Multiplication 

1.  £  of  26.  7.  1  of  56.  13.  f  of  32.  19.  8  x  |. 

2.  i  of  30.  8.  |  of  72.  14.  f  of  48.  20.  12  x  |. 

3.  £  of  32.  9.  |  of  32.  15.  TV  of  32.  21.  9  x  J. 

4.  i  of  72.  10.  |  of  44.  16.  t\  of  32.  22.  9  x  f . 

5.  J  of  36.  11.  £  of  48.  17.  8  x  J.  23.  6  x  f . 

6.  i  of  84.  12.  J  of  96.  18.  8  x  |.  24.  6  x  T\. 

25.  At  the  rate  of  f  mi.  a  minute,  how  far  will  a  train  go 
in  4  min.  ? 

26.  How  much  is  £  of  48  ?    f  of  48  ft.?    |  of  $48  ?    f  of 
$480  ?    |  of  $4800  ? 

27.  If  a  room  is  32  ft.  long,  and  the  width  is  T7^  as  much, 
what  is  the  width  ? 

28.  An  inch  being  TJ^  ft.,  how  many  feet  in  48  in.  ?    in 
60  in.  ?    in  36  in.?    in  72  in.?    in  96  in.  ?    in  144  in.  ? 

67.  Multiplication 

2       3       2        3  1 

Think  of  -  of  -  as  -  of  - ,  or  -  •    Always  cancel  mentally  before 

o         o         j)          0  4 

you  multiply,  if  possible.      * 


1. 

frof  £. 

6. 

fcof 

I. 

11.  ; 

|of 

i 

16. 

f 

of 

f' 

2. 

\&\. 

7. 

frof 

f- 

12. 

|of 

1- 

17. 

1 

of 

f. 

3. 

K* 

8. 

Jof 

1- 

13. 

^of 

*• 

18. 

8 
f 

of 

8 

¥• 

4. 

frof*. 

9. 

*of 

t- 

14.  j 

fr<rf 

1- 

19. 

£ 

of 

|i 

5. 

frof  §. 

10. 

&°f 

3 

4' 

15.     ; 

^of 

• 
f' 

20. 

t 

of 

7- 

il 

FTnw  mm 

:>,h  is  1 

of  3 

:?     i 

of  ^  of 

a1? 

i   of 

£  of 

3  < 

if  4 

t? 

22.  A  foot  is  what  part  of  a  yard  ?    of  5  yd.  ?    of  7  yd.  ? 

23.  An  inch  is  what  part  of  a  foot  ?    \  ft.  is  what  part  of 
a  yard  ? 

24.  A  ruler  is  marked  in  quarters  of  an  inch,  and  each  of 
these  spaces  is  divided  into  thirds.   How  long  is  each  of  the 
small  divisions  ? 


MULTIPLICATION  91 

68.   Multiplication 


1. 

i  of  2. 

6-  i  of  81. 

11.  4  x  If. 

16.  2|  x  3. 

2. 

*of  £. 

7.  £  of  8§. 

12.  3  x  1§. 

17.  1$  x  8. 

3. 

i  of  24. 

8.  $  of  6|. 

13.  3i  x  4. 

18.  If  x  8. 

4. 

i  of  4|. 

9.  2x3j. 

14.  2i  x  6. 

19.  8  x  2\. 

5. 

i  of  6*. 

10.  3  x  2£. 

15.  2|  x  4. 

20.  8  x  If 

21.  What  is  the  area  of  a  square  whose  side  is  4  in.  ?  \  in.  ? 
6  in.?    l£  in.? 

22.  What  is  the  area  of  a  rectangle  2  in.  by  3  in.  ?    2  in. 
by  3J  in.? 

23.  If  the  side  of  a  square  is  2^  in.,what  is  the  perimeter  ? 

24.  If  a  book  is  1|  in.  thick,  how  high  will  be  a  pile  of 
4  such  books?    of  8  such  books  ? 

25.  If  a  board  is  1|  in.  thick,  what  will  be  the  height  of 
a  pile  of  4  such  boards  ?    of  8  such  boards  ? 

69.   Multiplication 


1-  i 

of  *• 

7. 

£ 

of 

3 

»• 

13. 

iof 

I- 

19. 

|of 

§• 

2.  ^ 

of  |. 

8. 

£ 

of 

1? 

14. 

|of 

2i. 

20. 

|  of 

2|- 

3-  i 

off. 

9. 

£ 

of 

1- 

15. 

f  of 

2|. 

21. 

|of 

4. 

4-  i 

ofi. 

10. 

f 

of 

f. 

16. 

f  of 

2i. 

22. 

1i  X 

4. 

5-  i 

off. 

11. 

f 

of 

5 

17. 

iof 

8 
3- 

23. 

f  of 

6. 

6.  i 

off. 

12. 

^ 

of 

i- 

18. 

iof 

2|- 

24. 

2^x 

6. 

25.  I  wish  to  make  a  drawing  ^  as  long  as  the  original. 
By  what  length  in  the  drawing  shall  I  represent  f  in.  in 
the  original  ?    \  in.  in  the  original  ? 

26.  I  wish  to  make  a  drawing  of  a  map  f  of.  its  original 
length.    By  what  length  in  the  drawing  shall  I  represent 
§  in.  in  the  original  ?    1§  in.  (or  |  in.)  in  the  original  ? 

27.  I  wish  to  make  a  floor  plan  of  a  room,  representing 
1  ft.  by  \  in.    The  floor  is  17  ft.  wide.    By  what  length  shall 
I  represent  the  width  of  the  room  ? 


COMMON 

FRACTIONS 

70. 

Division 

1. 

I*J^J«- 

J-*-3. 

11. 

§.      0 
^8. 

2. 

|  -H  3.  J>  _7. 

i-*-4- 

1  -  - 

f  -=-6. 

3. 

f  -5-  3.   '      8. 

•^   ~r~  O. 

13. 

|-j-6. 

4. 

$  -*-  4.         9. 

f  +  4. 

14. 

T\  -s-  6- 

5. 

A-j-2.  '     10. 

A  H-  6. 

15. 

A  --  10. 

92 


16.  TV+6. 

17.  tfV-5-3. 

18.  ^-^5- 

19.  T&-S-10. 
iD                  20.  sV-14. 

21.  Reduce  "-21  to  fourths  and  then  divide  by  3.    Divide 
3£  by  5. 

22.  Reduce  2j  to  thirds  and  then  divide  by  14.   Divide 
2§  by  4. 

23.  If  I  walk  4  mi.  in  1^  hr.,  in  what  fraction  of  an  hour 
do  I  walk  a  mile  ? 

24.  If  I  walk  5f  mi.  in  2  hr.,  what  is  my  rate  per  hour  ? 

25.  If  I  walk  3  mi.  in  1  hr.,  how  long  will  it  take  me  to 
walk  1  mi.  ?    ^  mi.  ?    ^  mi.  ?    f  mi.  ? 

71.    Division 

1.  1  -5-  £.   2       6.  7  -s-  £.  2  '    11.  \*-\.2*  16.  i  -f-  f 

2.  3  -=- 1.     i/     7.  6  -5-  |.      /  12.  ^  -r-  §.  */,/ 17.  §  -f-  ^. 

3.  1  -H  J.      y        8.    8  -5-  f .    ;   /,    13.    |  -r-  f  «t^  18.    li  H-  1. 

4-  T-^-i-<i  ^    9.  J-i-i.  'i      14.  jL-*-4.A?5  ^9-  ii-s-i- 

4      n       0  ^  J        I  87      >•  L.  d  J  . 

5.  8  --  f  T  w.  10.  i  -^-  i-  ^     it  |  •*•  |.  yf  20.  1J  H-  f.     ' 

21.  How  many  i-inch  lengths  are  there  in  2  in.  ?  in2iin.  ? 
in2ito.? 

22.  How  many  times  is  1\  in.  contained  in  5  in.  ?    |  in  5  ? 
|  in  5? 

23.  If  a  strip  of  carpet  is  f  yd.  wide  and  9  yd.  long,  it  is 
how  many  times  as  long  as  it  is  wide  ? 

24.  How  many  times  is  l£  contained  in  2§  ?    in  2§  +  £  ? 
in  3? 

25.  How  many  times  is  1J  contained  in  2|  ?    in  2£  ? 
in  5?    in  10? 


MULTIPLICATION  AND  DIVISION  93 

72.   Multiplication.   Aliquot  Parts 

Think  of  24  X  25^  as  24  x  $£,  or  $6.  Think  of  48  x  12^  as  48  x  $£, 
or  $6.  Think  of  36  x  50^  as  36  x  $|,  or  $18.  Think  of  36  x  75^  as 
36  x  $|,  or  §27. 

1.  28  x  50/.  5.  48  x  25/.  9.  72  x  12$/. 

2.  64  x  50/.  6.  88  x  25/.  10.  24  x  75/. 

3.  21  x  50/.  7.  32  x  12 1/.  11.  32  x  75/. 

4.  32  x  25/.  8.  56  x  12$/.  ^   12.  44  x  75/. 

13.  At  50/  each,  what  will  18  books  cost  ? 

14.  At  25/  each,  what  will  a  dozen  lamp  shades  cost  ? 

15.  At  75/  a  yard,  what  will  80  yd.  of  Brussels  carpet  cost  ? 

16.  At  12^X  a  yard,  what  will  64  ft.  of  picture  mold- 
ing cost  ? 

17.  At  12^/  a  yard,  what  will  24  yd.  of  gingham  cost? 
what  will  96  yards  cost  ? 

73.   Division.   Aliquot  Parts 

Think  of  $3  H-  $0.50  as  $3  -=-  §|,  or  as  2  x  3,  or  as  6. 
Think  of  §3  -r-  §0.25  as  $3  -^  $£,  or  as  4  x  3,  or  as  12. 
Think  of  $5  +  §0.12£  as  $5  -H  $},  or  as  8  x  5,  or  as  40. 

2 

Think  of  $6  -H  $0.75  as  $6  H-  $|,  or  as     X     ,  or  as  8. 

# 

1.  $5 -^  $0.50.  5.  $6-*- $0.25.  9.  $9  -*-  $0.12£. 

2.  $7  -=-$0.50.  6.  $8 --$0.25.  10.  $3  -^  $0.75. 

3.  $9  --$0.50.  7.  $6-*- $0.12$.  11.  $9  -=-  $0.75. 

4.  $4  -*-$0.25.  8.  $8  -f-  $0.12$.  12.  $12  •*- $0.75. 

13.  At  50/  each,  how  many  baskets  can  be  bought  for  $12  ? 

14.  At  25/  each,  how  many  fishing  rods  can  be  bought 
for  $7  ? 

15.  At  12$X  a  box,  how  many  boxes  of  berries  can  be 
bought  for  $2  ?    for  $2J  ? 

16.  At  75/  each,  how  many  books  can  be  bought  for  $6  ? 


94  DECIMAL  FRACTIONS 

IV.    DECIMAL  FRACTIONS 

74.   Reduction 

Think  of  .25  or  0.25  as  £fa>  or  ?•   Think  of  1.5  as  lr5^,  or  1|. 
Reduce  to  common  fractions  or  mixed  numbers  : 

1.  0.5.          4.  0.60.        7.  0.8.  10.  2.8.         13.  7.50. 

2.  0.50.        5.  0.4.          8.  0.75.         11.  3.5.         14.  2.20. 

3.  0.2.          6.  0.40.        9.  1.4.  12.  4.4.         15.  3.75. 

Reduce  to  dollars  and  common  fractions  of  a  dollar  : 

16.  $1.50.  20.  $2.40.  24.  $3.12^.  28.  $2.16§. 

17.  $1.25.  21.  $3.60.  25.  $1.33J.  29.  $3.37£. 

18.  $1.75.  22.  $5.20.  26.  $2.33£.  30.  $2.62£. 

19.  $1.20.  23.  $1.12£.  27.  $1.66|.  31.  $5.87£. 


75.   Reduction 

Think  of  2.8  as  2f,  or  -1/.    Think  of  1.75  as  If,  or  |. 
Reduce  to  improper  common  fractions  : 

1.  1.5.          3.  1.4.          5.  1.8.  7.  2.25.          9.  1.20. 

2.  1.2.          4.  1.6.          6.  3.5.  8.  1.75.        10.  1.40. 

Reduce  to  common  fractions  or  mixed  numbers  : 

11.  0.3.        14.  0.75.      17.  2.40.        20.  3.10.        23.  5.50. 

12.  0.30.      15.  0.10.      18.  2.25.        21.  3.5.          24.  7.75. 

13.  0.25.      16.  1.3.        19.  5.75.        22.  4.50.        25.  8.20. 

Reduce  to  improper  common  fractions  : 

26.  2.5.        28.  2.2.        30.  2.8.          32.  7.50.        34.  1.40. 

27.  4.5.        29.  2.4.        31.  4.50.        33.  3.20.        35.  1.75. 
36.  Express  32.12^  mi.  as  miles  and  a  common  fraction. 


REDUCTION  95 

76.  Reduction 

To  reduce  \  to  a  decimal  fraction,  think  of  multiplying  both  terms 
by  some  number  that  will  make  the  denominator  10,  100,  or  1000. 
Thus  £  =  y2^,  or  0.25. 

Reduce  to  decimal  fractions  : 

1.  f  4.  f.  7.  A-  10-  A-  13-  % 

2.  J.  5.  f.  8.  A-  11-  2i-  14-  7§- 

3.  f.  6.  |.  9.  A-  12-  3J.  15.  3f. 

Reduce  to  dollars  and  cents  : 

ic     4£  1 1         117     ^Sli        10     4fe  ~1  3  10     4fe  9  3  on     4  £»  3 

lo.    Jp-L^".       17.    Jpl^.      lo.    <B>-Lj.  IS/.    «fl>^5.  i4U.    <J?OTJ. 

21.  How  many  cents  in  $2i  ? 

22.  How  many  cents  in  $3f  ? 

23.  How  many  quarters  of  a  dollar  in  $2.50  ? 

24.  How  many  half  dollars  in  $2.50  ?    in  $7.50  ? 

77.  Reduction 

Reduce  to  decimal  fractions  : 

1.  i.  4.  f.  7.  f.  10.  ^.  13.  6f. 

2.  f.  5.  f.  8.  A-  11-  »i- 

31  fi7  Ql  19     74  1591       £~^" 

'    8*  O-    ~5'  "'    ~%~5'  *•"'     '  ~5'  *•*"'       5Tf* 

16.  Express  75|  mi.  as  miles  and  a  decimal. 

17.  Express  34^  mi.  as  miles  and  a  decimal. 

18.  Express  $2i  as  dollars  and  a  decimal ;  as  cents. 

19.  Express  $15|  as  dollars  and  a  decimal ;  as  cents. 

Express  as  the  sum  of  two  decimal  fractions  : 

20.  J.  +  f         22.  \  +  f .         24.  \  +  f .         26.  f  +  \. 

21.  £  +  4.         23.  £  +  J.         25.  i  +  f .         27.  f  +  f . 

28.  Express  2^  +  4|  as  the  sum  of  mixed  decimals. 

29.  A  train  travels  45|  mi.  an  hour.    Read  this  distance 
as  a  mixed  decimal. 


96  DECIMAL  FRACTIONS 

78.   Addition 

Add  the  following : 


1. 

.2 

5.  .08 

9.  .09 

13. 

.07 

17.  .006 

.7 

.06 

.09 

.07 

.120 

2. 

3 

6.  .5 

10.  .008 

14. 

.08 

18.  .009 

T9tf 

.7 

.005 

.03 

.128 

3. 

.3 

7.  .6 

11.  .1 

15. 

.009 

19.  .012 

.9 

.7 

.9 

.090 

.125 

4.  .7  8.  .05         12.  .9  16.  .007         20.  .015 

.9  .09  .6  .072  .125 

21.  How  much  is  0.8  in.  and  0.7  in.  ?    |  in.  and  f  in.  ? 

79.   Addition 

Add  the  following : 


1. 

.4 

4. 

.5 

7.  .5 

10. 

.20 

13. 

.575 

.5 

.6 

.25 

.95 

.003 

2. 

.3 

5. 

.05 

8.  .50 

11. 

.70 

14. 

.575 

.6 

.06 

.70 

.077 

.005 

3. 

.5 

6. 

.5 

9.  .50 

12. 

.300 

15. 

.575 

.5 

.06 

.75 

.033 

.025 

16.  Add  £  and  £ ;  add  0.75  and  0.25. 

17.  Add  $f  and  $}  ;  add  $0.75  and  $0.50. 

18.  Add  $£  and  $£ ;  add  $0.12^  and  $0.25. 

19.  Add  $£  and  $f ;  add  $0.33£  and  $0.66§. 


ADDITION  97 

80.  Addition 

Add  the  following : 

1.  1.1          4.  2.8  7.  1.7  10.  3.8  13.  .35 
_.8               ^8               1.3                 2.1  .16 

2.  1.4          5.  3.9          8.  1.8  11.  2.5  14.  .36 
_.6               _.§               1.4                 3.5  .17 

3.  1.7          6.  1.2          9.  2.6          12.  .25  15.  .42 
_^6               1.3               1.5                 .35  .19 

16.  How  much  is  0.25  in.  and  0.5  in.  ? 

17.  How  much  is  0.25  in.  and  f  in.  ? 

18.  The  three  sides  of  a  triangle  are  0.25  ft.,  0.2  ft.,  and 
0.24  ft.    What  is  the  perimeter  ? 

81.  Addition 

Add  the  following  : 

1.  .20          4.  .35          7.  1.3          10.  3.6  13.  2.60 
.35               .47               2.7                 2.6  3.50 

2.  .25          5.  .57          8.  1.3          11.  2.40  14.  2.60 
.35               .28               2.9                 3.40  3.80 

3.  .28          6.  1.3          9.  2.5  12.  2.50  15.  4.70 
.37               2^4               2.9                 3.50  3.45 

16.  Add  2.5  mi.,  3.3  mi.,  and  4.5  mi. 

17.  Add  $2.50  and  $3.50 ;  add  $2.50  and  $3.60. 

18.  If  my  purchases  amount  to  $4.80  and  $3.30,  what  is 
the  total  ? 


98  DECIMAL  FRACTIONS 

82.   Subtraction 

Subtract  the  following : 


1. 

1.8 

4. 

3.4 

7. 

2.0 

10. 

2.0 

13. 

6.3 

.5 

.5 

.7 

.6 

.9 

2. 

2.8 

5. 

5.6 

8. 

4.0 

11. 

2.3 

14. 

2.4 

.6 

.8 

.9 

.8 

.6 

3. 

3.4 

6. 

3.0 

9. 

3.0 

12. 

3.4 

15. 

3.1 

.4 

.4 

.8 

.7 

.8 

16.  What  number  must  be  added  to  5  to  make  8?    to 
0.5  to  make  0.8  ? 

17.  What  number  must  be  subtracted  from  11  to  leave  6  ? 
from  1.1  to  leave  0.6  ? 

83.   Subtraction 

Subtract  the  following  : 


1. 

1.6 

4. 

2. 

0 

7. 

3.5 

10. 

4 

,1 

13. 

6.1 

.5 

5 

.8 

.8 

1.7 

2. 

1.2 

5. 

3. 

0 

8. 

4.3 

11. 

5.3 

14. 

6.3 

.5 

_: 

7 

.5 

.4 

2.7 

3. 

2.3 

6. 

3. 

4 

9. 

4.2 

12. 

5 

.4 

15. 

7.8 

.6 

6 

.6 

.8 

3.9 

16.  What  number  must  be  added  to  0.5  to  make  0.6  ? 

17.  What  number  must  be  added  to  3  to  make  21  ?   to  0.3 
to  make  2.1  ? 

18.  What  number  must  be  subtracted  from  23  to  make  8  ? 
from  2.3  to  make  0.8  ?   from  0.23  to  make  0.08  ? 


SUBTRACTION  99 

84.   Subtraction 

To  subtract  .54  from  2.61  mentally,  first  subtract  .5,  leaving  2.11, 
and  then  subtract  .04. 

Subtract  the  following  : 

1.  1.25          3.  1.25         5.  1.35          7.  1.20  9.  2.05 

.20  .15  .06  .08  .05 


2.  1.25 
.05 

4.  1.35 
.35 

6.  1.50 
.05 

8.  1.20 
.18 

10.  2.00 
.50 

11.  How  much  is  $1.25  —  $0.50? 

12.  If  I  owe  $0.75  and  pay  $5,  how  much  change  should 
I  receive  ? 

13.  If  I  have  $0.37,  how  much  must  I  add  to  it  to  have 
$0.50  ? 

85.   Subtraction 

Subtract  the  following : 


1.  2.5 

3.  2.5 

5.  3.4 

7.  2.25 

9.  3.56 

1.3 

1.8 

1.9 

.27 

.37 

2.  2.5 

4.  3.2 

6.  2.25 

8.  2.42 

10.  3.71 

1.5 

1.6 

.07 

.29 

2.46 

11.  If  I  have  $2.25  and  spend  8/,  how  much  is  left? 
How  much  is  left  if  I  spend  17/  more  ? 

12.  If  I  have  $2.50  and  make  purchases  amounting  to 
25/  and  65  ef,  how  much  is  left  ? 

13.  If  I  have  $3.50  and  spend  $0.75,  how  much  is  left  ? 

14.  If  I  have  $5  and  spend  $4.30,  how  much  is  left  ? 

15.  If  I  have  $10  and  spend  $5.75,  how  much  is  left? 

16.  If  I  have  $25  and  spend  $12.50,  how  much  is  left  ? 


1.  2  x  .2. 

6.  3  x  .8. 

11.  5  x  .2. 

2.  2  x  .5. 

7.  4  x  .2. 

12.  6  x  .8. 

3.  2x.7. 

8.  4  x  .5. 

13.  9  x  .1. 

4.  3  x  .3. 

9.  4x.9. 

14.  8x.5. 

5.  3  x  .5. 

10.  5  x  .1. 

15.  9x.2. 

100  DECIMAL  FRACTIONS 

86.    Multiplication 

16.  2  x  .09. 

17.  3  x  .09. 

18.  4  x  .12. 

19.  7x.ll. 

20.  8  x  .20. 

21.  If  a  side  of  a  square  is  .25  in.,  what  is  the  perimeter  ? 

22.  If  each  side  of  a  triangle  is  .3£  yd.,  what  is  the 
perimeter  ? 

23.  If  a  strip  of  carpet  is  .75  yd.  wide,  how  wide  will  be 
the  width  of  2  strips  laid  side  by  side  ?    of  4  strips  ? 

24.  If  a  sheet  of  cardboard  is  0.3  in.  thick,  how  thick  will 
a  pile  of  9  sheets  be  ? 

25.  If  a  piece  of  glass  is  0.6  in.  thick,  how  thick  will  6 
layers  of  this  glass  be  ? 

87.   Multiplication  by  Tens 

Think  of  40  x  .8  as  4  x  10  x  .8,  or  4  x  8,  or  32.     Similarly,  think 
of  70  x  1.1  as  7  x  11,  or  77. 

1.  10  x  .4.  5.  20  x  .5.  9.  30  x  .6.  13.  10  x  1.5. 

2.  10  x  .5.  6.  30  x  .3.  10.  60  x  .1.  14.  40  x  2.5. 

3.  10  x  .8.  7.  30  x  .4.  11.  70  x  .2.  15.  50  x  1.1. 

4.  20  x  .4.  8.  30  x  .5.  12.  80  x  .3.  16.  80  x  2.5. 

17.  At  25/  each,  what  will  40  neckties  cost? 

18.  At  50,^  each,  what  will  20  knives  cost  ? 

19.  At  75/  each,  what  will  40  baskets  cost  ? 

20.  If  a  board  is  0.8  in.  thick,  how  high  will  be  a  pile  of 
60  such  boards  ? 

21.  There  are  50  sheets  of  blotting  paper  in  a  pile,  each 
sheet  being  0.05  in.  thick.    Find  the  thickness  of  the  pile. 

22.  There  are  60  sheets  of  paper  in  a  pile,  each  sheet 
being  0.02  in.  thick.    Find  the  thickness  of  the  pile. 


MULTIPLICATION  101 

88.   Multiplication 


1.  3  x  .2. 

6.  6  x  .3. 

11.  5x.9. 

16.  8  x  .07. 

2.  5  x  .2. 

7.  6  x  .5. 

12.  7x.6. 

17.  3  x  1.1. 

3.  2  x  .5. 

8.  6  x  .7. 

13.  5  x  .06. 

18.  3x1.3. 

4.  8x.7. 

9.  5  x  .8. 

14.  5  x  .09. 

19.  3  x  1.5. 

5.  3x.6 

10.  8x.5. 

15.  3  x  .08. 

20.  3x2.5. 

f21.  If  one  tennis  ball  costs  22/,  what  will  5  cost  ? 

22.  If  one  tennis  racquet  costs  $2.50,  what  will  3  cost  ? 

23.  At  45/  each,  what  will  three  arithmetics  cost  ? 

24.  If  a  board  is  0.9  in.  thick,  what  is  the  thickness  of  a 
pile  of  4  such  boards  ? 

25.  If  each  side  of  a  pentagon  (5-sided  figure)  is  0.7  in., 
what  is  the  perimeter  ? 

26.  If  each  link  in  a  chain  is  0.25  in.  long,  how  long  is  a 
chain  of  30  links  ? 

89.   Multiplication 


1.  6  x  .7. 
2.  .7  of  6. 
3.  5  x  .9. 
4.  .9  of  5. 

5.  .3  of  4. 
6.  .5  of  8. 

7.  .6  of  7. 
8.  .9  of  8. 

9.  12  x  .2. 
10.  .2  of  12. 
11.  1.2  x  2. 
12.  2  x  1.2. 

13.  .2  of  15. 
14.  2  x  1.5. 
15.  1.5x2. 
16.  15  x  .2. 

17.  How  much  is  10  x  .8  ?    10  x  .08  ?   10  x  $0.08? 

18.  How  much  is  30  x  8  ?  30  x.  8?  30x.08?  30  x.  008? 

19.  How  much  will  40  quarts  of  berries  cost  at  9/  a  quart  ? 

20.  How  much  will  75  postage  stamps  cost  at  2/  each  ? 

21.  How  much  will  50  postage  stamps  cost  at  5/  each? 

22.  At  $50  an  acre,  what  will  0.8  of  an   acre  of  land 
cost? 

23.  At  $75  an  acre,  what  will  0.8  of  an  acre  of  land 
cost? 

24.  At  $90  a  front  foot,  how  much  will  a  city  lot  cost 
that  has  a  frontage  of  30.1  ft.  ? 


102  DECIMAL  FRACTIONS 

90.   Division 


1.  0.6-2. 
2.  0.9  -  3. 
3.  1.2-5-2. 
4.  1.5-3. 

5.  1.8  -H  6. 
6.  2.1-5-7. 

7.  2.5  -5-  5. 
8.  6.4-*-  8. 

9.  .06-5-3. 
10.  .08-5-2. 
11.  .24-5-8. 
12.  .63-5-9. 

13.  .72-*-8. 

14.  .81  -  9. 
15.  .63-5-3. 

16.  .81  -5-  3. 

17.  If  8  qt.  of  berries  cost  $0.48,  what  does  1  qt.  cost  ? 
What  do  3  qt.  cost  ? 

18.  If  a  train  travels  2.1  mi.  in  3  min.,  what  is  its  rate 
per  minute  ? 

19.  If  a  man  is  driving  at  the  rate  of  0.66  mi.  in  3  min., 
what  is  his  rate  per  minute  ? 

20.  If  an  automobile  is  traveling  at  the  rate  of  0.62  mi. 
in  2  min.,  what  is  its  rate  per  minute  ? 

21.  If  an  automobile  is  traveling  at  the  rate  of  0.9  mi. 
in  3  min.,  what  is  its  rate  per  minute  ?  per  hour  ? 

91.  Division  by  Tens 

Think  of  .9  -f-  30  as  .09  -r-  3,  or  .03. 

1.  3  -5- 10.       5.  3.1  -5- 10.        9.  6  -s- 10.        13.  8  -5-  10. 

2.  7  -5- 10.       6.  7.3  -f- 10.      10.  6  -5-  20.       14.  8  -=-  20. 

3.  .3  -5- 10.       7.  .21  -5- 10.      11.  6  -5-  30.        15.  8  -t-  40. 

4.  .7-5-10.      8.  .41-5-10.       12.  .6-5-30.       16.  .8-5-40. 

17.  If  20  yd.  of  cloth  cost  $14,  what  does  1  yd.  cost  ? 

18.  If  50  yd.  of  lace  cost  $75,  what  does  1  yd.  cost  ? 

19.  If  30  schoolbooks  cost  $7.50,  what  does  1  school- 
book  cost  ? 

20.  If  a  train  travels  0.8  mi.  in  40  sec.,  what  is  its  rate 
per  second  ? 

21.  If  20  strips  of  wall  paper  measure  10  yd.  when  hung 
side  by  side,  how  wide  is  each  strip  ? 

22.  If  30  strips  of  carpet  measure  22.5  yd.,  when  laid 
side  by  side,  how  wide  is  each  strip  ? 


DIVISION  103 

92.   Division 


1.  .8-*-  4. 
2.  1.2  H-  4. 

5.  1.5  -s-  5. 
6.  2.5  -v-  5. 

9.  .45-8-5. 

10.  .50  H-  5. 

13.  4-s-lO. 
14.  .4  _=_  10. 

3.  1.6  -5-  8. 

7.  3.5  -r-  7. 

11.  .75  -H  5. 

15.  6  -r-  20. 

4.  2.4  -j-  6. 

8.  .63  -j-  7. 

12.  .72-i-9. 

16.  .6  --20. 

17.  If  10  sheets  of  paper  are  together  0.4  in.  thick,  what 
is  the  average  thickness  ?  f> 

18.  If  a  train  travels  20  mi.  in  16  min.,  what  is  the 
average  time  per  mile  ? 

19.  If  a  train  travels  12  mi.  in  20  min.,  what  is  the  rate 
per  minute  ? 

20.  If  a  train  travels  2.73  mi.  in  3  min.,  what  is  its  rate 
per  minute  ? 

21.  If  a  manufacturer  uses  153  yd.  of  cloth  in  making  30 
waists,  how  many  yards  does  he  use  for  each  ? 

93.   Division 

In  dividing  .9  by  .3,  think  of  both  numbers  as  multiplied  by  10, 
giving  9  H-  3,  or  3. 

1.  $6n-$3.  5.  1.2.-J-.4.  9.  2.8 -5- .7.  13.  .28 -5- .7. 

2.  ^  --  JQ.  6.  2.5  -}-  .5.  10.  8.1  -s-  .9.  14.  .81  -s-  .9. 

3.  .6  -5-  .3.  7.  3.6  -s-  .9.  11.  7.2  -=-  .8.  15.  .72  H-  .8. 

4.  .8  -«-  .2.   .  8.  3.5  H-  .7.  12.  5.6  -*-  .7.  16.  .56  +  .7. 

17.  By  what  must  .4  be  multiplied  to  equal  2.8  ? 

18.  How  many  times  is  0.1  in.  contained  in  3.8  in.? 

19.  How  long  will  it  take  a  train  traveling  0.7  mi.  a 
minute  to  go  14.7  mi.  ? 

20.  How  long  will  it  take  a  train  traveling  0.8  mi.  a 
minute  to  go  32.8  mi.  ? 

21.  An  excavation  9.6  yd.  long  and  .8  yd.  wide  is  how 
many  times  as  long  as  wide  ?    If  a  plan  of  it  is  drawn  in 
which  the  width  is  1  in.,  what  should  be  the  length  ? 


104  DENOMINATE  NUMBERS 

V.   DENOMINATE  NUMBERS 

94.  Reduction  Descending 

Think  of  3  ft.  4  in.  as  the  sum  of  3  x  12  in.  and  4  in.,  or  40  in. 
Reduce  : 

1.  1  ft.  to  inches.  6.  2  Ib.  to  ounces. 

2.  8  ft.  to  inches.  7.  1  ft.  7  in.  to  inches. 

3.  3  yd.  to  feet.  8.  4  ft.  11  in.  to  inches. 

4.  9  yd.  to  feet.  9.  5  yd.  2  ft.  to  feet. 

5.  4  bu.  to  pecks.  10.  4  gal.  1  qt.  to  quarts. 

11.  How  mai/y  cubic  feet  in  1  cu.  yd.?    in  2  cu.  yd.? 

12.  How  many  square  inches  in  1  sq.  ft.?   in  10  sq.  ft.? 
in  100  sq.  ft.  ? 

13.  If  1  sq.  ft.  of  concrete  flooring  costs  8  ct.,  how  much 
will  1  sq.  yd.  cost  ? 

95.  Reduction  Ascending 

Think  of  48  in.  as  ff  ft.,  or  4  ft.    In  the  same  way  think  of  245^ 


Reduce : 

1.  27  ft.  to  yards.  7.  120  in.  to  feet. 

2.  60  in.  to  feet.  8.  360  sec.  to  minutes. 

3.  12  pt.  to  quarts.  9.  160  oz.  to  pounds. 

4.  24  qt.  to  gallons.  10.  21 OO/  to  dollars. 

5.  32  oz.  to  pounds.  11.  120  qt.  to  gallons. 

6.  120  min.  to  hours.  12.  18  in.  to  feet  and  inches. 

13.  What  part  of  a  foot  is  1  in.  ?    ^  in.  ? 

14.  How  many  feet  in  48  in.  ?   How  many  yards  ? 

15.  If  a  milk  man  has  25  qt.  of  milk  left  from  his  day's 
sales,  how  many  gallons  has  he  left  ?    Express  the  result 
as  gallons  and  a  fraction ;  as  gallons  and  quarts. 


REDUCTION  105 

96.  Reduction 

1.  30  sec.  =  ?  min.  9.  12  hr.  =  ?  da. 

2.  £  hr.  =  ?  min.  10.  4  hr.  =  ?  da. 

3.  15  sec.  =  ?  min.  11.  36  hr.  =  ?  da. 

4.  i  hr.  =  ?  min.  12.  48  hr.  =  ?  da. 

5.  45  sec.  =  ?  min.  13.  14  da.  =  ?  wk. 

6.  |  hr.  =  ?  min.  14.  21  da.  =  ?  wk. 

7.  20  min.  =  ?  hr.  15.  6  mo.  =  ?  yr. 

8.  15  min.  =  ?  hr.  16.  18  mo.  =  ?  yr. 

17.  If  I  reach  the  station  15  min.  before  train  time  and 
the  train  is  f  hr.  late,  how  long  must  I  w;  't? 

18.  If  school  closes  in  4  wk.,  how  man}    ""ays  will  this 
be  ?   How  many  school  days  ? 

19.  If  we  recite  £  hr.,  how  many  minutes  is  this  ?    After 
half  the  time  is  gone,  how  many  minutes  remain  ? 

97.  Reduction 

1.  1  yr.  =  ?  da.  6.  4  mo.  =  ?  yr. 

2.  1  yr.  =  ?  wk.  7.  8  mo.  =  ?  yr. 

3.  1  yr.  =  ?  mo.  8.  18  mo.  =  ?  yr. 

4.  £  yr.  =  ?  mo.  9.  £  yr.  =  ?  wk. 

5.  l\  yr.  =  ?  mo.  10.  |  yr.  =  ?  wk. 

11.  Allowing  30  da.  to  the  month,  how  many  days  in. 
6  mo.?    in  12  mo.?    How  many  days  are  there  really  in 
a  year? 

12.  How  many  days  has  February  in  an  ordinary  year  ? 
in  a  leap  year  ?   How  many  days  has  March  ?    How  many 
days  in  February  and  March  together  ? 

13.  How  many  days  from  May  10  to  June  10  ?    from 
June  10  to  July  10  ? 

14.  How  many  days  from  February  5  to  March  5  in  an 
ordinary  year  ?    in  a  leap  year  ? 


106  DENOMINATE  NUMBERS 

98.   Reduction 
Express  as  inches  : 

1.  3  ft.  3.  10  ft.  5.  2$.  ft.          7.  2  yd. 

2.  4  ft.  4.  2  ft.  4  in.       6.  £  yd.  8.  1  yd.  4  in. 

Express  as  feet  or  as  feet  and  fractions  : 

9.  24  in.       11.  5  yd.  13.  48  in.        15.   \  yd. 

10.  36  in.       12.  18  in.  14.  30  in.        16.  2j  yd. 

Express  as  yards  or  as  yards  and  fractions  : 

17.  36  in.        18.  18  in.  19.  9  ft.          20.  10£  ft. 

21.  Express  32  oz.  as  pounds ;  also  24  oz. 

22.  Express  8  oz.  as  a  fraction  of  a  pound ;  also  12  oz. 

23.  Express  20  pk.  as  bushels ;  20  bu.  as  pecks. 

99.   Fractions  of  Denominate  Numbers 

1.  Express  y1^  of  20  ft.  as  feet  ;  as  inches. 

2.  Express  \  of  50  Ib.  as  pounds  ;  as  ounces. 

3.  Express  \  of  40  yd.  as  yards  ;  as  feet. 

4.  Express  \  of  36  in.  as  inches  ;  as  feet. 

5.  Express  \  of  40  bu.  as  bushels  ;  as  pecks. 

6.  Express  \  of  60  gal.  as  gallons  ;  as  quarts. 

7.  Express  |  of  48  ft.  as  feet ;  as  yards. 

8.  Express  f  of  20  yd.  as  yards ;  as  feet. 

9.  Express  f  of  48  oz.  as  ounces ;  as  pounds. 

10.  Express  the  sum  of  3  ft.  and  1  ft.  6  in.  as  feet  and 
inches  ;  as  feet  and  a  fraction ;  as  inches. 

11.  Express  4x8  oz.  as  ounces ;  as  pounds.   Also  express 
4  x  2  Ib.  8  oz.  as  pounds. 

12.  Express  45  yd.  -=-  9  as  yards  ;  as  feet.    Also  express 
90  yd.  -5-  9  as  yards  ;  as  feet ;  as  inches. 


REVIEW  107 

100.   Review 

1.  A  farmer  wishes  to  fill  in  a  piece  of  low  land  having 
an  area  of  2700  sq.  ft.,  raising  the  level  on  an  average  of  1  ft. 
How  many  loads  (cubic  yards)  of  earth  will  it  take  ? 

2.  In   Ex.  1    suppose   the   low  land   had   an   area   of 
8100  sq.  ft.   How  many  loads  would  it  take  ? 

3.  A  farmer  who  had  a  large  poultry  yard  fed  his  hens 
168  Ib.  of  corn  in  April.    How  many  bushels  did  he  feed 
them,  at  56  Ib.  to  the  bushel  ? 

4.  A  farmer  has  a  20-acre  meadow  from  which  he  cut 
last  year  2|  tons  of  hay  to  the  acre.    How  many  tons  of 
hay  did  he  cut  ? 

5.  A  farmer  had  a  field  of  35  acres  from  which  he  cut 
3  tons  to  the  acre.    How  many  tons  of  hay  did  he  cut  ? 

6.  A  farmer  sows  10  acres  of  oats,  using  1\  bu.  to  the 
acre.    How  many  bushels  of  seed  does  he  use  ?    What  is  it 
worth  at  $1  a  bushel  ? 

7.  A  farmer  uses  40  Ib.  of  seed  per  acre  for  a  20-acre 
meadow,  of  which  one  fifth  by  weight  is  red  clover.    How 
many  pounds  of  red  clover  will  he  need  in  all  ? 

8.  For  a  meadow  of  30  acres  a  farmer  uses  43  Ib.  of  seed 
to  the  acre.    How  many  pounds  does  he  use  ? 

9.  A  farmer  has  apiece  of  pasture  land  40  rd.  by  20  rd. 
How  many  acres  are  there  in  this  pasture  ? 

10.  A   farmer  has   a  10-acre  lot  of   corn  that  yielded 
32  bu.  to  the  acre.    This  he  sold  at  60/  a  bushel.    How 
much  did  he  receive  for  the  corn  ? 

11.  A  farmer  has  25  cows  worth  $60  each.    How  much 
are  they  all  worth  ?     How  much  would  they  all  be  worth 
at  $64  each? 

12.  A  farmer  has  a  rectangular  field  that  contains  25 
acres.    It  is  80  rd.  long.    How  wide  is  it?   What  is  the 
perimeter  of  the  field  ? 


108  DENOMINATE  NUMBERS 

13.  Last  year  a  gardener  had  3  acres  of  potatoes  and 
raised  200  bu.  to  the  acre.     How  many  bushels  did  he 
raise  in  all  ? 

14.  If  he  sold  these  potatoes  at  60/  a  bushel,  how  much 
did  he  get  for  them  all  ? 

15.  Potatoes  weigh  60  Ib.  to  the  bushel.    What  was  the 
weight  of  his  potato  crop  ? 

16.  For  spraying  his  potato  plants  he  uses  1  Ib.  of  Paris 
green  to  100  gal.  of  water.    Since  1  gal.  of  water  weighs 
8.3  Ib.,  the  weight  of  the  Paris  green  is  what  part  of  the 
weight  of  water  ? 

17.  He  soaked  his  seed  potatoes  in  a  solution  of  1  pt.  of 
formalin  to  25  gal.  of  water,  to  keep  off  the  potato  scab. 
What  part  of  the  solution  is  formalin  ? 

18.  If  |  of  the  weight  of  potatoes  is  water,  and  if  a 
bushel  of  potatoes  weighs  60  Ib.,  what  is  the  weight  of 
water  in  a  bushel  of  potatoes  ? 

19.  He  had  2  acres  of  celery,  and  the  yield  was  1550  doz. 
heads  to  the  acre.    How  many  dozen  did  he  have  in  all  ? 

20.  He  bought  seed  for  1000  celery  plants  at  24/  an  ounce. 
Allowing  an  ounce  of  seed  to  2000  plants,  how  much  did 
the  seed  cost  ? 

21.  When  wheat  costs  $1.12^  a  bushel,  how  much  will 
100  bu.  cost  ?   1000  bu.  ?   2000  bu.  ? 

22.  If  wheat  is  worth  $1  a  bushel,  how  much  will  the 
yield  of  a  100-acre  field  be  worth  if  the  average  yield  is 
25  bu.  per  acre  ? 

23.  If  wheat  is  worth  $1.10  a  bushel,  how  much  will  the 
yield  of  a  50-acre  field  be  worth  if  the  average  yield  is  20 
bu.  per  acre  ? 

24.  If  wheat  is  worth  $1.12^  a  bushel,  how  much  will 
the  yield  of  80  acres  be  worth  if  the  average  yield  is  25 
bu.  per  acre  ? 


CHAPTER  III 
I.    FUNDAMENTAL  OPERATIONS 

1.   Reading  Numbers 

Read  the  following  : 

1.  0.123.  5.  0.245.                           9.  XLI. 

2.  100.023.  6.  200.045.  10.  XLIX. 

3.  0.0004.  7.  0.1204.  11.  CCXIX. 

4.  1,244,244.  8.  31,000,000,000.  12.  DCXC. 

13.  DCXCIX.  15.  MCMXIL 

14.  CDXCIX.  16.  MDCCCCXII. 

The  forms  in  Exercises  15  and  16  are  both  allowed. 

17.  What  do  you  mean  by  a  decimal  point  ? 

18.  What  is  the  difference  between  an  order  and  &  period? 

2.   Various  Units 

1.  What  is  the  unit  when  you  are  counting  dollars  ? 
cents  ?    dozens  ?    fourths  ? 

2.  Count  from  ^  to  1,  using  -fa  as  the  unit. 

3.  If  you  use  1  ft.  as  the  unit,  how  many  units  in  2  ft.? 
If  you  use  1  in.  as  the  unit,  how  many  units  in  2  ft.  ? 

4.  State  four  units  of  length ;  four  units  of  capacity. 

5.  State  four  units  of  area;  four  units  of  cubic  measure. 

6.  Taking  the  dozen  as  the  unit,  how  many  such  units 
in  72?    in  144? 

7.  What  is  meant  by  a  unit  fraction  ?   Give  three  illus- 
trations. 

109 


110  FUNDAMENTAL  OPERATIONS 

3.   Addition  of  Integers 
Add  the  following : 


1. 

28 

4. 

39 

7. 

57 

10. 

77 

13. 

127 

22 

32 

24 

36 

36 

2. 

28 

5. 

42 

8. 

56 

11. 

83 

14. 

132 

29 

29 

38 

48 

49 

3. 

37 

6. 

46 

9. 

74 

12. 

88 

15. 

258 

26 

37 

28 

35 

37 

16.  If  the  sides  of  a  triangle  are  27  in.,  36  in.,  33  in., 
what  is  the  perimeter  ?   How  many  feet  ? 

17.  If  I  make  purchases  amounting  to  $1.25,  55/,  and 
20/,  what  is  the  total  amount  I  spend  ? 


4.   Addition  of  Decimals 

Add  the  following  : 


1. 

3.8 

4.  4.5 

7. 

.72 

10. 

.78 

13. 

9.36 

.9 

2.6 

.6 

.38 

6. 

2. 

3.8 

5.  7.3 

8. 

.34 

11. 

1.24 

14. 

4.23 

1.9 

4.8 

.17 

.09 

.38 

3. 

3.7 

6.  .27 

9. 

.53 

12. 

1.72 

15. 

.576 

1.8 

.09 

.62 

.7 

.029 

16.  Add  2.3  mi.  and  7.9  mi. 

17.  Add  $2.75,  $4,  and  $0.50. 

18.  Add  8.4  in.,  6.2  in.,  and  5.4  in. 

19.  Add  14.9  in.,  4.1  in.,  and  5  in.   Express  the  sum  as  feet. 


ADDITION  111 

5.   Addition  of  Common  Fractions 

1.  i  +  I-  5-  i  +  f  •  9-  I  +  i-  13-  H  +  §• 

2-  I  +  I-  6.  |  +  |.  10.  |  +  f  .  14.  2fc  +  ^. 

3.  i  +  i.  7.  f  +  J.  11.  TV  +  |.  15.  3|  +  ft. 

4.  |  +  f  .  8.  |  +  i.  12.  ft  +  |.  16.  4f  +  ft. 

17.  How  much  is  5|  in.  and  4^  in.  ? 

18.  Express  as  feet  9J  in.  -f  1|  in.  +  ll£  in.  +  1^  in. 

19.  A  picture  frame  is  8|  in.  by  3£  in.    What  length  of 
molding  does  it  contain  ? 

20.  A  board  is  6£  in.  wide  and  £  in.  thick.    What  is  the 
length  of  a  string  that  will  just  reach  around  it? 

21.  If  a  room  is  28^  ft.  long  and  11|  ft.  wide,  what  is 
the  perimeter  ? 

22.  If  a  cask  contains  2i  gal.  of  sirup,  and  we  add  If  gal. 
and  then  add  |  gal.,  how  much  does  it  then  contain  ? 

6.   Addition  of  Denominate  Numbers 

Add  the  following  : 

1.  32  ft.  8  in.  5.  15  Ib.  10  oz.  9.  17  gal.  2  qt. 

6  5  1         9  9         3 

2.  38  ft.  4  in.  6.  26  Ib.  14  oz.  10.  28  bu.  3  pk. 

7  9  3         7  6        3 


3. 

29  ft.  3  in. 

7.  32yd. 

2ft. 

11.  36  gal. 

4pt. 

7     11 

8 

2 

8 

5 

4. 

9  ft.  8  in. 

8.  27yd. 

29  in. 

12.  25  gal. 

3qt. 

1       1 

6 

7 

6 

3 

13.  7  ft.  4  in.  +  2  ft.  8  in.  +  3  ft.  6  in. 


112  FUNDAMENTAL  OPERATIONS 

7.   Review.   Grocer's  Problems 

Think  of  1750  +  375  as  2050  +  75,  or  2125.    In  general,  in  oral 
addition,  it  is  more  convenient  to  begin  at  the  left. 

1.  A  grocer  paid  $2.44  for  a  dozen  bottles  of  olives  and 
$14.20  for  a  gross  of  macaroni  in  packages.    What  was  the 
amount  of  his  bill  ? 

2.  He  also  bought   $18.60  worth   of   spice  and  $4.80 
worth  of  mustard.    What  did  these  cost  ? 

3.  He  paid  $223.50  for  a  lot  of  tea  and  $62.50  for  some 
coffee.    What  did  these  cost  ? 

4.  He  paid  $11.75  for  a  gross  of  gelatin  in  packages 
and  $44.25  for  some  prunes.    What  did  these  cost  ? 

5.  He  bought   $42.60  worth   of   canned  peaches,  and 
$40.50  worth  of  canned  pears.     What  was  his  bill  ? 

6.  He  bought  5  crates  of  eggs  at  $8  and  $75  worth  of 
butter.    How  much  did  he  pay  for  both  ? 

7.  He  paid  $72.75  for  some  honey  and  $57  for  some 
maple  sirup.    How  much  did  he  pay  for  both  ? 

8.  He  bought  720  Ib.  of  domino  sugar  and  490  Ib.  of 
maple  sugar.    W7hat  was  the  total  weight  ? 

9.  If  one  box  contains  196  oranges  and  another  contains 
180,  how  many  oranges  are  there  in  the  two  boxes  ? 

10.  If  the  grocer  has  27  qt.  of  strawberries,  16  qt.  of 
raspberries,   and   17  qt.  of  currants,  how  many  quarts  of 
berries  has  he  in  all  ? 

11.  If,  in  taking  an  inventory,  he  finds  that  he  has  on 
one  shelf  29  bottles  of  cucumbers,  16  bottles  of  olives,  and 
35  bottles  of  pickled  peaches,  how  many  bottles  has  he  of 
all  three  ? 

12.  A  grocer  bought  a  quantity  of  sugar  for  4|/  a  pound 
and  sold  it  for  5|X  a  pound.    How  much  did  he  gain  on 
each  pound  ?    How  much  would  he  gain  on  1000  Ib.  ?  How 
much  would  he  gain  011  2000  Ib.  ? 


SUBTRACTION  113 

8.  Subtraction  of  Integers 
Subtract  the  following  : 

1.  39  4.  42  7.  55  10.  65  13.  205 
16                 25                 28                 28  _90 

2.  36  5.  44  8.  57  11.  125  14.  204 
16                 28                 39                   18  94 

3.  32  6.  54  9.  63  12.  125  15.  207 

16  37  26  28  98 

16.  If  a  room  32  ft.  long  has  a  rug  18  ft.  long  on  the 
floor,  how  much  of  the  length  is  not  covered  ? 

17.  If  a  man  having  $225  in  the  bank  deposits  $65  to-day 
and  draws  out  $75  to-morrow,  how  much  will  be  left  ? 

9.  Subtraction  of  Decimals 

Subtract  the  folloiving  : 

1.  2.7  4.  5.4  7.  .47  10.  .70  13.  30.2 

.9  3.5  .28  .29  2.6 


2.  3.2 

5.  7.5 

8.  .52 

11.  2.04 

14.  .463 

1.6 

4.9 

.37 

.65 

.058 

3.  4.3 

6.  .32 

9.  .66 

12.  .208 

15.  .090 

2.8 

.09 

.48 

.072 

.018 

16.  If  I  have  $3.06  and  spend  88/,  how  much  is  left  ? 

17.  If  the  distance  between  two  stations  is  23.14  mi.,  and 
a  train  has  gone  6.2  mi.  from  one  station  towards  the  other, 
what  is  the  remaining  distance  ? 


114  FUNDAMENTAL  OPERATIONS 

10.   Subtraction  of  Common  Fractions 

!•*•->  5-    T5if  -  i-  9-    i  -  TV' 

*•*-*•       6-  I  -  TV       10.  i  -  tV       I*.  |  -  ^. 

3.  i  -  i-          7.   i  -  ^.          11.  |  -  TV         15.  3^  -  i. 


199  1  1  fi     71          7 

IS  ~~  ¥•  "'    Tff  —  ¥•  **•    Tff         1*  10.     <  ¥  —  ?. 

17.  I  have  a  piece  of  wood  8|  in.  long,  of  which  I  need 
6|  in.  for  a  box  I  am  making.    How  much  of  the  length 
will  be  left  ? 

18.  I  have  a  piece  of  wire  £  in.  in  diameter  that  I  wish 
to  file  down  to  fit  a  hole  ^  in.  in  diameter.    How  much 
must  it  be  filed  down  ? 

19.  In  laying  a  tile  floor  with  tile  4£  in.  square  a  work- 
man came  to  the  edge  where  he  needed  a  tile  3£  in.  wide. 
How  much  must  be  chipped  off  from  the  tile  to  reduce  it  to 
this  width  ? 

11.   Subtraction  of  Denominate  Numbers 

Subtract  the  following  : 

1.  3  ft.  7  in.  4.  23  ft.  8  in.  7.  23  gal.  1  qt. 

8  7      10  17          2 


2.  12  ft.  6  in.  5.  36  rd.  10  ft.  8.  46  bu.  2  pk. 

3       9  8        12  26         3 

3.  37  Ib.  4  oz.  6.  17  mi.  16  rd.         9.  27  wk.  4  da. 
27       6  8         36  12         5 

10.  If  a  carpenter  saws  2  ft.  8  in.  from  a  board  10  ft.  6  in. 
long,  how  much  is  left  ? 

11.  If  a  piece  of  flannel  43 £  yd.  long  shrinks  22  in.  in 
washing,  how  long  is  it  then  ? 


SUBTRACTION  115 

12.   Review 

1.  After  87  days  of  an  ordinary  year  have  passed,  how 
many  days  remain  ? 

2.  A  note  having  120  days  to  run  has  already  run  86 
days.    How  many  more  days  before  it  matures  ? 

3.  If  a  man  weighing  164^  Ib.  loses  8  Ib.  12  oz.,  how 
much  does  he  then  weigh  ? 

4.  A  picture  covering  1  sq.  ft.  is  so  framed  that  6.5 
sq.  in.  is  covered  by  the  molding.    How  much  is  not  cov- 
ered by  the  molding  ? 

5.  The  steam   gauge  of  a  boiler  shows  a  pressure  of 
121  Ib.    If  it  is  reduced  38  Ib.,  what  is  the  pressure  then  ? 

6.  A  grindstone  that  had  a  radius  of  13.4  in.  has  had 
1.9  in.  ground  off.    What  is  now  its  radius  ? 

7.  If  I  have  $42  in  the  bank  and  deposit  $17  more 
and  $40  more,  and  the  next  day  take  out  $35,  how  much 
have  I  left? 

8.  The  perimeter  of  a  triangle  is  42  in.,  and  two  of  the 
sides  are  15  in.  and  16  in.    What  is  the  length  of  the  other 
side? 

9.  If  a  dealer  buys  14  qt.   of  berries  from  one  man, 
27  qt.  from  another,  and  16  qt.  from  another,  and  sells 
53  qt.,  how  many  quarts  has  he  left  ? 

10.  The  distance  from  Chicago  to  Denver  is  1083  mi.,  and 
from  Chicago  to  Omaha  it  is  503  mi.    How  far  is  it  from 
Omaha  to  Denver  ? 

11.  If  a  milk  dealer  having  32  gal.  of  milk  sells  5  gal.  at 
a  hotel,  and  3  qt.  at  one  house  and  2  qt.  at  another,  how 
much  has  he  left  ? 

12.  If  a  carpenter  wishes  to  make  a  sill  for  a  house,  and 
splices  together  two  pieces  of  timber  18  ft.  long  and  14  ft. 
long,  losing  l£  ft.  by   splicing,  and  then  saws  off  2^  ft., 
what  is  the  remaining  length  ? 


116  FUNDAMENTAL  OPERATIONS 

13.   Multiplication  of  Integers 


1.  3  x  31. 

2.  2x35. 
3.  4  x  45. 

4.  2  x  76. 

5.  3x38. 
6.  3  x  74. 
7.  4x42. 
8.  4  x  67. 

9.  5x27. 
10.  6  x  37. 
11.  7x35. 

12.  7  x  72. 

13.  8  x  29. 
14.  8  x  64. 
15.  9x23. 
16.  9x81. 

17.  How  many  dimes  in  a  dollar  ?  in  $15  ? 

18.  How  many  inches  in  a  yard  ?    in  5  yd.  ? 

19.  How  many  square  inches  in  2  sq.  ft.  ? 

20.  How  many  cubic  feet  in  2  cu.  yd.  ? 

21.  How  many  pints  in  a  quart?    in  a  gallon?    in  15 
gal.  ?    in  30  gal.  ? 

22.  How  many  pints  in  a  quart  ?  in  a  peck  ?  in  a  bushel  ? 
in  6  bu.  ?    in  10  bu.  ? 

23.  If  each  side  of  an  octagon  (8-sided  figure)  is  17  in., 
what  is  the  perimeter  ? 

14.   Multiplication  of  Decimals 

1.  6  x  5/.  5.  2  x  .27.  9.  5  x  .32.  13.  .2  of  20. 

2.  6  x  .05.  6.  3  x  .32.  10.  5  x  .37.  14.  .3  of  25. 

3.  7  x  .08.  7.  4  x  .51.  11.  6  x  2.1.  15.  .4  of  32. 

4.  8  x  .06.  8.  4  x  .53.  12.  7  x  2.2.  16.  .6  of  70. 

17.  How  much  is  .3  of  7  ?  T3«j  of  TV  ?  .3  of  .7  ? 

18.  How  much  is  .3  of  9  ?  t\  of  TO<J  ?  -3  of  -9  ?  -3  of  -8  ? 

19.  .3  of  .2.      21.  .5  of  .8.       23.  .2  of  .8.        25.  .4  of  .8. 

20.  .4  of  .6.      22.  .7  of  .4.       24.  .3  of  .5.        26.  .6  of  .9. 

27.  Compare  .2  of  .7  of  100,  and  .7  of  .2  of  100. 

28.  From  a  steel  plate  .17  in.  thick  6  strips  are  cut  and 
placed  one  on  top  of  another.   How  high  is  the  pile  ? 

i.  A  gardener  has  .8  of  an  acre  of  land,  .3  of  which  he 
devotes  to  onions.  What  part  of  an  acre  is  devoted  to 
onions  ?  How  much  does  this  lack  of  being  \  of  an  acre  ? 
of  being  1  acre  ? 


MULTIPLICATION  117 

15.   Multiplication  of  Common  Fractions 

1.  |  of  16.  6.  28  x  f .  11.  f  of  J.  16.  f  of  .8. 

2.  §  of  36.  7.  f  of  f .  12.  W  off  17.  £  of  y5-. 

3.  f  of  25.  8.  f  of  f .  13.  |  of  |f .  18.  $  of  7J. 

4.  |  of  72.  9.  §  of  f.  14.  |  of  §f.  19.  £  of  1'. 

5.  15  x  f .  10.  |  of  f .  15.  |  of  TV  20.  |  of  5J. 

21.  Find  ^  of  f  of  f  of  f  by  rapid  cancellation. 

22.  J  of  f  of  f .         23.  f  of  f  of  40.         24.  1  of  £  of  64. 

25.  If  I  need  for  a  box  cover  a  piece  of  wood  |  as  thick 
as  a  £-in.  board,  how  thick  is  the  cover  ? 

O  ' 

26.  A  box  is  ^  as  wide  as  it  is  long,  and  £  as  deep  as  it 
is  wide.    It  is  3  ft.  long.    How  deep  is  it  ? 

27.  A  carpenter  in  making  a  plan  of  a  box  represents  a 
dimension  by  a  line  |  of  its  original  length.    If  the  box  is 
2§  ft.  long,  how  long  is  the  drawing  of  it  ? 

16.   Multiplication  of  Denominate  Numbers 

1.  12  x  2  ft.  1  in.  5.  16  x  2  gal.  1  qt. 

2.  12  x  3  ft.  6  in.  6.  25  x  4  ft.  1  in. 

3.  20  x  5  Ib.  1  oz.  7.  2£  x  10  mi.  4  rd. 

4.  16  x  2  Ib.  2  oz.  8.  3^  x  6  ft.  2  in. 
9.  Express  f  of  16  qt.  as  gallons  and  quarts. 

10.  Express  24  times  |  bu.  as  bushels ;  as  pecks. 

11.  At  $1.60  a  yard,  what  will  27  in.  of  velvet  cost  ? 

12.  At  $1.28  a  yard,  what  will  £  yd.  of  silk  cost  ?    f  yd.  ? 

13.  At  $75  an  acre,  what  will  \  of  an  acre  of  land  cost  ? 

14.  If  a  piece  of  work  requires  4  wk.  5  da.  and  another 
requires  twice  as  long,  how  much  time  does  the  second 
require,  allowing  6  working  days  to  the  week  ? 

15.  If  a  piece  of  work  requires  7  da.  5  hr.  and  another 
requires  twice  as  long,  how  much  time  does  the  second 
require,  allowing  8  hours  to  the  working  day  ? 


118  FUNDAMENTAL  OPERATIONS 

17.   Review 

1.  At  35/  a  pound,  what  will  9  Ib.  of  butter  cost  ? 

2.  At  $5  a  barrel,  what  will  18  bbl.  of  flour  cost  ? 

3.  At  15/  a  dozen,  what  will  8  doz.  paper  pads  cost  ? 

4.  At  $7.25  a  hundred,  what  will  300  Ib.  of  meat  cost  ? 

5.  At  20  bricks  to  the  hod,  how  many  bricks  in  26  hods  ? 

6.  At  25  Ib.  each,  what  will  10  chests  of  tea  weigh  ? 
11  chests  ? 

7.  At  24/  a  word,  what  will  a  9-word  telegram  from 
London  to  New  York  cost  ? 

8.  At  200  Ib.  to  the  cubic  foot,  what  will  0.2  cu.  ft.  of  a 
certain  kind  of  stone  weigh  ? 

9.  A  gallon  contains  231  cu.  in.    How  many  cubic  inches 
does  0.1  gal.  contain  ?    0.2  gal.  ?    0.3  gal.  ? 

10.  If  there  are  34  pieces  of  cloth  in  a  bale,  how  many 
pieces  in  8  bales  ? 

11.  A  farmer  paid  $1.50  a  rod  for  some  ditching.    How 
much  did  he  pay  for  9  rd.  ? 

12.  A  train  averages  40.7  mi.  an  hour  for  3  hr.    What  is 
the  distance  covered  in  that  time  ? 

13.  If  sound  travels  1120  ft.  a  second,  how  far  will  it 
travel  in  2  sec.?    in  0.1  sec.? 

14.  If  a  man's  step  in  rapid  walking  averages  28  in.,  how 
many  inches  will  he  walk  in  taking  9  steps  ? 

ft£}5.  If  you  are  in  school  5  hours  a  day  and  200  days  in  a 
year,  how  many  hours  are  you  in  school  in  each  year  ? 

16.  From  Ex.  15,  how  many  minutes  are  you  in  school 
in  each  year  ? 

17.  From  Ex.  15,  how  many  days  of  the  year  are  you 
not  in  school  ? 

18.  From  Ex.  15,  how  many  days  in  8  school  years? 
How  many  minutes  does  a  boy  or  girl  spend  in  school  in 
8  years  if  there  are  no  absences  ? 


DIVISION  119 

18.   Division  of  Integers 


I  48  +  2. 

7.  84-5-4. 

13.  $636  -=-6. 

2.  480-5-2. 

8.  840-=-  4. 

14.  $726-6. 

3.  484-2. 

9.  844-4. 

15.  $637  -5-  7. 

4.  63-3. 

10.  95-5-5. 

16.  $648-$! 

5.  630  +  3. 

11.  950-5. 

17.  $576  +  $! 

6.  639  +  3. 

12.  955-5. 

18.  $612-$! 

19.  If  7  horses  cost  $770,  what  is  the  average  price  ? 

20.  If  7  horses  cost  $805,  what  is  the  average  price  ? 

21.  At  $7  each,  how  many  writing  desks  can  be  bought 
for  $861  ? 

22.  If  we  divide  336  sq.  rd.  of  land  into  8  equal  building 
lots,  what  is  the  area  of  each  ? 

23.  If  $1224  is  divided  equally  among  9  men,  what  is 
the  share  of  each  ? 


19.   Division  of  Integers 

1. 

220 

+  10. 

6. 

372  + 

12. 

11. 

340 

-4- 

17. 

2. 

220 

+  11. 

7. 

260  + 

13. 

12. 

198 

+ 

18. 

3. 

231 

+  11. 

8. 

294  + 

14. 

13. 

150 

ft. 

+ 

50. 

4. 

240 

+  12. 

9. 

330  + 

15. 

14. 

200 

yd 

-25. 

5. 

252 

+  12. 

10. 

176  + 

16. 

15. 

300 

in.  + 

75  in. 

In  each  of  the  following  express  the  quotient  as  an  integer 
and  a  fraction  : 

16.  2001  +  4.          18.  3665  +  6.          20.  6484  -  8. 

17.  2001  +  5.          19.  3516  +  7.          21.  6312  +  9. 

22.  How  many  feet  in  264  in.?  in  270  in.? 

23.  How  many  pounds  in  80  oz.  ?  in  88  oz.  ? 

24.  How  many  yards  in  396  in.?  in  414  in.? 

25.  How  many  weeks  in  154  da.?  in  161  da".? 

26.  How  many  hours  in  120  min.  ?  in  150  min.  ? 


120  FUNDAMENTAL  OPERATIONS 

20.  Division  of  Decimals 

1.  16.4 -j- 2.  6.  .217 --7.  11.  31.5-^15. 

2.  1.71  -s-  3.  7.  33.6  +  8.  12.  .336  -=-  16. 

3.  14.4 ---4.  8.  40.5 --9.  13.  6-5-3;  $6  -=-  $3. 

4.  1.45  -r-  5.  9.  5.04  -=-  9.  14.  T%  -r-  ^  ;  .6  ->-  .3. 

5.  .144  --6.  10.  1.21-5-11.  15.  33.3 --.3. 

Think  of  .63  -4-  .3  as  6.3  -f-  3.    That  is,  multiply  both  by  10  before 
dividing. 

16.  36.6  H-  .6.  18.  6.56  -=-  .8.  20.  7.38  -5-  .9. 

17.  50.4  -=-.7.  19.  7.36-^.8.  21.  .828 -- .9. 

22.  If  the  perimeter  of  a  square  is  28.8   in.,  what  is 
the  side  ? 

23.  If  a  man  travels  1.32  mi.  in  3  min.  on  his  bicycle, 
what  is  his  rate  per  minute  ? 

21.  Division  of  Decimals 

Think  of  .064  -r-  .32  as  6.4  -=-  32.    That  is,  multiply  both  by  10  often 
enough  to  make  the  divisor  integral. 

1.  1.44 -5-.  12.  5.  3.25 -.25.  9.  73.5  -H  .35. 

2.  2.73  -^  .13.  6.  1.50  -=-  .75.  10.  $17.60  -*-  $0.16. 

3.  1.65  -=-.15.  7.  28.8  -H  .12.  11.  2.64  in.  -=-  .24  in. 

4.  2.75  H-  .25.  8.  52.5  H-  .25.  12.  6.72  mi.  -=-  .32  mi. 

13.  Divide  2  x  4.5  by  0.3. 

14.  If  a  train  travels  0.99  mi.  in  1.1  min.,  what  is  its 
rate  per  minute  ? 

15.  If  a  train  is  traveling  at  the  rate  of  0.8  mi.  per 
minute,  how  long  will  it  take  it  to  go  2.4  mi.  ? 

16.  At  16/  each,  how  many  bottles  of  ink  can  be  bought 
for  $1.44  ? 

17.  At  17/  a  yard,  how  many  yards  of  cloth  can  be 
bought  for  $3.40  ?    for  $3.57  ? 


DIVISION  121 

22.   Division  of  Common  Fractions 

1.  f  -H  f         4.  |  -i- 1.         7.  if  +  A.         10.  ^  +  ft. 

2.  |  -i-  f .          5.  i  H-  |.         8.  |i  1-  &.         11.  ^  4-  f . 

3.  |  -I- -f .          6.  f  +  f .         9.  A  -  TV         12.  |  -H  ?V 

13.  How  much  is  |  ^- 1?  l$-*-f  ?  H-s-0.75?  1.5-^0.75? 

14.  How  much  is  42  H-  7  ?   \2-  H-  |  ?    V  +  i  ?  5i  •*•  1  ? 
5.25  -j-  .87 £  ? 

15.  How  many  boards,  each  |  in.  thick,  must  be  placed 
one  on  top  of  another  to  make  a  pile  3  in.  high  ?  1  ft.  high  ? 

16.  If  a  piece  of  cardboard  is  ^\  in.  thick,  how  many 
pieces  are  there  in  a  pile  6  in.  high  ? 

17.  If  a  strip  of  carpet  is  f  yd.  wide,  how  many  strips 
will  be  needed  for  a  room  6  yd.  wide  ? 

18.  If  a  strip  of  wall  paper  is  \  yd.  wide,  how  many 
strips  will  be  needed  for  a  space  1\  yd.  wide  ? 

23.   Division  of  Denominate  Numbers 

1.  244  ft.  8  in.  -=-4.  5.  2  ft.  H-  8  in. 

2.  372  gal.  6  pt.  -=-6.  6.  3  ft.  4  in.  -H  10  in. 

3.  205  mi.  30  rd.  --5.  7.  1  yd.  14  in.  --  5  in. 

4.  355  ft.  9  in.  H-  3.  8.  2  Ib.  8  oz.  H-  20  oz. 
9.  Divide  the  sum  of  2  ft.  8  in.  and  1  ft.  6  in.  by  4. 

10.  If  a  train  travels  2  mi.  in  3  min.  10  sec.,  what  is  its 
time  per  mile  ? 

11.  If  a  train  travels  1.8  mi.  in  2  min.,  what  is  its  rate 
per  minute  ? 

12.  If  a  train  travels  1.75  mi.  in  2  min.  20  sec.,  what  is 
its  rate  per  minute  ?    (1.75  mi.  =  |  mi. ;   2  min.  20  sec.  = 
2^  min.  or  £  min.) 

13.  Allowing  8  in.  for  the  length  of  a  brick  and  its 
mortar,  how  many  lengths  of  brick  in  a  wall  that  is  4  ft. 
long  ?    40  ft.  long  ? 


122  FUNDAMENTAL  OPERATIONS 

24.   Review 

1.  At  60/  a  yard,  what  will  |  yd.  of  silk  cost  ? 

2.  At  $1.40  a  yard,  what  will  2£  yd.  of  velvet  cost  ? 

3.  At  $1.10  a  yard,  what  will  10^  yd.  of  carpet  cost  ? 

4.  At  $1.20  a  yard,  what  will  16  yd.  of  pongee  cost? 
what  will  2^  yd.  of  pongee  cost  ? 

5.  At  32/  a  yard,  what  will  7  yd.  of  madras  cost  ? 
what  will  1\  yd.  of  madras  cost  ?  *)f~jZ 

6.  I  bought  32  yd.  of  cloth  and  have  used  ^ftof  it.    How 
many  yards  have  I  used  ? 

7.  I  bought  34  yd.  of  cloth  and  have  used  f  of  it.    How 
many  yards  have  I  used  ? 

8.  I  paid  $15  for  some  silk  at  $1.25  a  yard.    How  many 
yards  did  I  buy  ?    ($^°-  -=-  $|.) 

9.  I  paid  $9  for  some  silk  at  $1.12^  a  yard.   How  many 
yards  did  I  buy  ? 

10.  If  a  piece  of  linen  contains  52  yd.,  and  a  merchant 
has  7  pieces  in  stock,  how  many  yards  has  he  ? 

11.  If  a  merchant  has  9  pieces  of  a  certain  kind  of  cloth, 
each  containing  41  yd.,  how  many  yards  of  this  kind  of 
cloth  has  he  ? 

12.  A  jngrchant  has  a  niece  of  cloth  containing  48  yd. 
e  sells  f  61  it,  and  then  J  3f  the  rest.    What  is  the  rest 

worth  at  $1  a  yard  ? 

13.  A  merchant  bought  1000  yd.  of  flannel  at  48/  a  yard 
.  and  sold  it  all  at  \  more  than  he  paid  for  it  ?    How  much 

did  he  gain  ? 

14.  A  clothing  manufacturer  bought  3000  yd.  of  cloth  at 
$1.50  a  yard  and  paid  $1000  down.    How  much  did  he  still 
owe? 

15.  A  manufacturer  sold  to  a  dealer  2500  yd.  of  cloth  for 
$1000,  and  the  dealer  sold  it  at  50/  a  yard.    How  much 
profit  did  he  make  ? 


MEASURES  123 

II.   MEASURES 
25.   Reduction 


Reduce  to  inches  : 


1.  9ft.  4.  9yd.  7.  9ft.  Gin.        10.  9yd.  Gin. 

2.  lift.         5.  llyd.        8.  11  ft.  8  in.      11.  11  yd.  4  in. 

3.  10^  ft.       6.  10^  yd.      9.  lyd.  1ft.        12.  2yd.  1ft. 

Reduce  to  feet  : 

13.  60 in.      15.  132  in.     17.  10 mi.  19.  Ird.  Gin. 

14.  120  in.    16.  27yd.       18.  10  rd.  20.  1  rd.  18  in. 

Reduce  to  yards  : 

21.  72  in.      22.  72ft.        23.  2rd.  24.  Imi. 

25.  Wall  paper  is  ^  yd.  wide.    How  many  inches  ? 

26.   Reduction 

Reduce  to  ounces : 

1.  71b.          3.  91b.  5.  125  Ib.  7.  3^1b. 

2.  11  Ib.        4.  25  Ib.         6.  21b.8oz.          8.  31b.  2oz. 

Reduce  to  pounds  : 
9.  48  oz.      10.  40  oz.        11.  f  T.  12.  3  T. 

Reduce  to  tons  or  fractions  of  a  ton : 

13.  4000  Ib.      14.  60,000  Ib.     15.  1500  Ib.      16.  3500  Ib. 

17.  How  much  will  7  T.  500  Ib.  of  coal  cost  at  $5  a  ton  ? 

18.  If  50  Ib.  of  candy  is  put  up  in  1-ounce  packages,  how 
many  packages  are  there  ? 

19.  If  a  cooking  recipe  calls  for  1  oz.  of  sugar  to  a  person, 
how  many  pounds  must  be  allowed  in  preparing  the  article 
for  40  persons  ? 


124  MEASURES 

27.  Review 

When  there  is  an  operation  like  —      — ,  do  not  multiply  until  you 

36 

have  canceled  as  much  as  possible.    It  is  easier  to  reduce  \5-  than  J^-, 
besides  the  saving  in  multiplication. 

1.  Half  a  dozen  chairs  are  being  upholstered,  and  each 
takes  30  in.  of  gimp.    How  many  yards  are  needed  ? 

2.  A  room  is  16  ft.  long  and  12  ft.  wide.    How  many 
yards  of  matting  1  yd.  wide  are  required  for  the  floor  ? 

3.  A  room  16  ft.  long  and  12  ft.  wide  is  to  have  a  carpet 
with  a  border.    How  many  yards  in  the  border  ? 

4.  Some  table  doilies  are  9  in.  square,  excluding  the  lace 
border.    If  4^  in.  extra  are  allowed  for  each  corner,  how 
many  yards  of  lace  are  needed  for  a  dozen  doilies  ? 

5.  A  carpet  rug  is  8  ft.  long  and  6  ft.  wide,  including  the 
border.    How  many  yards  of  border  has  it  ? 

6.  A  housekeeper  is  making  a  dozen  pairs  of  sheets,  each 
requiring  7  ft.  of  material  in  length  and  two  breadths  of 
material  in  width.    How  many  yards  are  needed? 

7.  Two  chairs  are  being  upholstered,  and  each  has  fringe 
around  the  bottom.    The  chairs  are  2  ft.  6  in.  on  the  front, 
and  20  in.  on  each  of  the  other  three  sides.    How  many 
yards  of  fringe  are  needed  for  both  chairs  ? 

8.  Some  curtains  8  ft.  long  and  a  yard  wide  are  to  have  a 
tassel  fringe  down  one  edge  and  across  the  bottom.    There 
are  six  of  these  curtains  in  a  room.   How  many  yards  of  the 
fringe  are  needed  ? 

9.  Some  window  curtains  are  to  hang  8  ft.  6  in.,  the  bot- 
toms being  made  of  lace,  9  in.  wide,  and  the  rest  being  cur- 
tain material  bought  by  the  yard.    There  are  four  windows 
in  the  room,  and  each  has  two  curtains.    How  many  yards  of 
curtain  material  are  needed  for  each  window,  aside  from 
the  lace  ?    for  all  four  windows  ? 


REDUCTION  125 

i 

28.  Reduction 

Seduce  to  pints : 

1.  25  qt.  3.  5  qt.  1  pt.       5.  3$  qt.  7.  2  gal.  2$  qt. 

2.  15  gal.          4.  6  gal.  2  qt.      6.  6  J  gal.         8.  20^  gal. 

Reduce  to  quarts  : 

9.  28  pt.         12.  37  pt.  15.  12$  gal.  *  18.  22  pk. 

10.  54  pt.         13.  15  gal.          16.  31$  gal.     19.  12$  pk. 

11.  25  pt.         14.  27  gal.          17.  15  pk.        20.  5pk.2qt. 

Reduce  to  gallons : 
21.  64  pt.         22.  80  pt.  23.  64  qt.        24.  80  qt. 

Reduce  to  pecks  : 
25.  15  bu.         26.  64  qt.  27.  25$  bu.      28.  100  qt. 

29.  Reduction 

Reduce  to  square  inches  : 
1.  2  sq.  ft.          2.  $  sq.  ft.        3.  ^  sq.  ft.     4.  10  sq.  ft. 

Reduce  to  square  feet : 
5.  5  sq.  yd.         6.  $  sq.  yd.       7.  288  sq.  in.    8.  2$  sq.  yd. 

Reduce  to  square  yards  : 
9.  54  sq.  ft.     10.  108  sq.  ft.     11.  81  sq.  ft.     12.  180  sq.  ft. 

Reduce  to  acres : 
13.  320  sq.  rd.  14.  80  sq.  rd.    15.  40sq.rd.   16.  640  sq.  rd. 

Reduce  to  cubic  feet  : 
17.  1728cu.in.  18.  2  cu.  yd.     19.  lOcu.yd.  20.  11  cu.  yd. 


126  MEASURES 

30.  Reduction 

Seduce  to  seconds  : 

1.  2  min.          2.  2j  min.        3.  11  min.      4.  1  hr. 

Reduce  to  minutes : 
5.  180  sec.  ^    6.  300  sec.       7.  2  hr.  8.  2£  hr. 

Reduce  to  hours : 
9.  240  min.    10.  420  min.    11.  90  min.    12.  4  da. 

Reduce  to  days  : 

13.  48  hr.        14.  120  hr.       15.  12  wk.     16.  2  wk.  12  hr. 

Reduce  to  weeks : 

17.  49  da.        18.  2  yr.  19.  84  da.      20.  56  da. 

31.  Reduction 

Reduce  to  seconds : 
1.  3'.  2.  3' 30".         3.  9'.  4.  1°. 

Reduce  to  minutes  : 
5.  3°.  6.  360".  7.  2°  30'.        8.  90°. 

Reduce  to  degrees  : 

9.  120'.  10.  3600".        11.  540'.         12.  90'. 

13.  How  many  degrees  in  l£  right  angles  ? 

14.  How  many  minutes  in  1  right  angle  ? 

15.  How  many  degrees  in  half  a  right  angle  ? 

16.  How  many  degrees  in  half  a  circumference  ? 

17.  How  many  degrees  of  latitude  from  the  equator  to 
the  north  pole  ? 


REDUCTION  127 

32.   Review 

1.  How  many  years  in  36  mo.?  in  104  wk. ? 

2.  How  many  months  in  4  yr.  ?  in  20  yr.  ? 

3.  How  many  days  from  February  7  to  March  7  ? 

4.  How  many  days  from  March  7  to  April  7  ?    from 
March  7  to  April  15? 

5.  If  a  recitation  in  arithmetic  lasts  40  inin.,  how  many 
seconds  does  it  last  ?   What  part  of  an  hour  ? 

6.  How  many  degrees  in  •£$  of  a  circumference  ?    Ex- 
press this  in  minutes. 

7.  If  a  train  makes  1  mi.  in  90  sec.,  how  many  minutes 
will  it  take  to  go  8  mi.  ? 

8.  Express  the  difference  between  9°  and  520'  in  min- 
utes ;  in  a  fraction  of  a  degree. 

9.  At  3  o'clock  how  many  degrees  are  there  in  the  angle 
made  by  the  two  hands  of  a  clock  ?    How  many  at  4  o'clock  ? 
at  2  o'clock  ? 

10.  The  sum  of  the  three  angles  of  a  triangle  is  always 
equal  to  two  right  angles.    In  an  equilateral  triangle  the 
angles  are  all  equal.    How  many  degrees  in  each  ? 

11.  If  there  are  200  school  days  in  a  school  year,  how 
many  weeks  is  this,  at  5  school  days  to  the  week  ?   How 
many  weeks  does  this  leave  for  vacation  ? 

12.  When  you  walk  diagonally  across  a  square  field,  how 
many  degrees  in  the  angle  that  your  path  makes  with  the 
side  of  the  field  ? 

13.  The  sum  of  the  angles  of  a  quadrilateral  (four-sided 
figure)  is  always  360°.    Suppose  three  of  these  angles  are 
80°,  110°,  and  70°.   What  is  the  size  of  the  fourth  angle  ? 

14.  When  the  horizontal  shadow  of  a  tree  is  just  as  long 
as  the  height  of  the  tree,  how  many  degrees  in  the  angle 
made  by  the  shadow  and  a  line  drawn  from  its  end  to  the 
top  of  the  tree  ? 


128  MEASURES 

33.  Perimeters 

Find  the  perimeters  of  triangles  whose  sides  are : 

1.  3  ft.,  4  ft.,  5  ft.  4.  5|  in.,  3J  in.,  4£  in. 

2.  3^  ft,  3£  ft.,  3£  ft.  5.  2  ft.,  27  in.,  3  ft. 

3.  4^  in.,  4i  in.,  3£  in.  6.  2  yd.,  5  ft.,  If  yd. 

Find  the  perimeters  of  squares  whose  sides  are : 

7.  8  in.  10.  3  ft.  6  in.^         13.  2.2  in. 

8.  l\  ft.  i  11.  4  ft.  9  in.  14.  3.25  in. 

9.  2  ft.  3  in.  '        12.  5  ft.  10  in.        15.  4.50  in. 

Find   the  perimeters  of  parallelograms    two    of  whose 
sides  are : 

16.  4  in.,  8  in.         18.  18  in.,  9  in.       20.  3^  yd.,  2  ft. 

17.  5  in.,  11  in.       19.  2  ft.  7  in.,  5  in.  21.  2  ft.,  2l£  in. 

34.  Rectangles 

Find  the  areas  of  rectangles  two  of  whose  sides  are  : 

1.  7  ft.,  8  ft.  *  5.  \  mi.,  5  mi.  9.  10  in.,  36  in. 

2.  5  ft.,  14  ft.  6.  a  mi.,  6  mi.  10.  10  in.,  1  yd. 

3.  7  in.,  13  in.  7.  \  ft,  2  ft.  11.  30  in.,  10  in. 

4.  \  mi.,  I  mi.  8.  6  in.,  2  ft.  12.  2  ft.  6  in.,  10  in. 

Find  the  areas  of  squares  whose  sides  are : 

13.  30  in.  15.  2  ft  6  in.          17.  1§  ft. 

14.  2£  ft  16.  20  in.  18.  1  ft  8  in. 

Find  the  lengths  of  rectangles,  with  areas  and  widths  as 

here  given  : 

It)  VI  1 

19.  50  sq.  in.,  5  in,    20.  51  sq.  in.,  3  in.    21.  77  sq.  ft,  11  ft. 

22.  If  the  perimeter  of  a  square  is  36  in.,  how  long  is 
each  side  ?   What  is  the  area  ? 

<\  ^ 


RECTANGLES  129 

35.  Rectangles 

Find  the  areas  of  the  following  rectangles  in  acres : 

1.  1  ch.  by  10  ch.  6.  8  ch.  by  15  ch. 

2.  6  ch.  by  10  ch.  7.  10  rd.  by  16  rd. 

3.  5  ch.  by  8  ch.  8.  20  rd.  by  32  rd. 

4.  5  ch.  by  12  ch.  9.  2$.  ch.  by  4  ch. 

5.  6  ch.  by  15  ch.  10.  7^  ch.  by  8  ch. 

11.  How  many  square  yards  in  a  rectangle  6  ft.  by  12  ft.  ? 

12.  What  is  a  field  worth  that  is  5  ch.  long  and  4  ch. 
wide,  at  $65  an  acre  ? 

13.  What  is  a  field  worth  that  is  40  rd.  long  and  12  rd. 
wide,  at  $70  an  acre  ? 

14.  Two  fields  have  equal  perimeters,  40  ch.  each.    One 
field  is  a  square  and  the  other  is  a  rectangle  12  ch.  long. 
What  is  the  area  of  each  field  ? 

36.  Rectangles 

Find  the  lengths  of  rectangles,  with  areas  and  widths  as 
here  given : 

1.  56  sq.  in.,  7  in.  5.  12  sq.  yd.,  9  ft. 

2.  154  sq.  in.,  11  in.  6.  1  sq.  rd.,  16^  ft. 

3.  2  A.,  4  ch.  7.  1  sq.  yd.,  18  in. 

4.  .1  sq.  ft.,  8  in.  8.  ^  sq.  ft.,  9  in. 

v 
Find  the  widths  of  rectangles,  with  areas  and  lengths  as 

here  given  : 

9.  90  sq.  in.,  10  in.  12.  144  sq.  in.,  16  in. 

10.  320  sq.  rd.,  20  rd.  13.  288  sq.  rd.,  32  rd. 

11.  540  sq.  yd.,  27  yd.  14.  640  sq.  yd.,  32  yd. 

15.  Which  has  the  greater  area,  a  square  whose  perim- 
eter is  36  in.  or  a  rectangle  7  in.  by  12  in.  ? 


130  MEASURES 

37.   Parallelograms 

Find  the  areas  of  parallelograms,  with  bases  and  altitudes 
as  here  given  : 

1.  3  ft.,  7  ft.  4.  7£  ft.,  2  ft.  7.  4i  ft.,  4  ft. 

2.  3  in.,  17  in.          5.  6£  ft.,  4  ft.  8.  5£  ft,  2  ft. 

3.  28  ft.,  3  ft.          6.  6  ft.  6  in.,  4  ft.      9.  5  ft.  3  in.,  2  ft. 

Find  the  altitudes  of  parallelograms,  with  areas  and  bases 
as  here  given  : 

10.  18  sq.  in.,  9  in.     12.  25  sq.  ft,  10  ft.   14.  51  sq.  in.,  17  in. 

11.  18  sq.  in.,  4  in.     13.  36  sq.  in.,  9  in.     15.  69  sq.  in.,  23  in. 

Find  the  bases  of  parallelograms,  with  areas  and  altitudes 
as  here  given  : 

16.  144 sq. in.,  1ft    18.  288 sq. in., 4ft.    20.  5 sq. in., 2 Jin. 

17.  288 sq. in.,  1ft    19.  38 sq. in.,  19 in.    21.  llsq.in.,5£in. 

38.   Triangles 

Find  the  areas  of  triangles  whose  bases  and  altitudes  are : 

1.  4  in.,  8  in.  5.  5  ft,  14  ft.  9.  1  mi.,  £  mi. 

2.  5  in.,  6  in.  6.  3  ft,  27  ft.  10.  12  in.,  20  in. 

3.  5  in.,  3  in.  7.  J  mi.,  1  mi.  11.  1  ft.,  20  in. 

4.  3  ft,  12  ft.  8.  ^  mi.,  3  mi.  12.  1  ft.,  1  ft.  8  in. 

Find  the  bases  of  triangles,  with  areas  and  altitudes  as  here 
given  : 

13.  4  sq.  ft,  2  ft.  16.  5  sq.  mi.,  2  mi. 

14.  8  sq.  in.,  8  in.  5.  17.  7  sq.  yd.,  14  yd. 

15.  15  sq.  yd.,  6  yd.  18.  35  sq.  ft,  10  ft 

19.  A  triangle  has  an  area  of  12  sq.  in.  and  a  base  of  1  ft. 
What  is  the  altitude  ? 


REVIEW  131 

39.   Review 

1.  What  is  the  altitude  of  a  triangle  with  area  1  sq.  in. 
and  base  1  in.  ? 

2.  What  is  the  altitude  of  a  triangle  with  area  l£  sq.  in. 
and  base  3  in.  ? 

3.  What  is  the  base  of  a  triangle  with  area  10  sq.  ft. 
and  altitude  2  ft.  ? 

4.  The  gable  of  a  house  is  a  triangle  with  base  35  ft. 
and  altitude  10  ft.    What  is  the  area  of  the  gable  ? 

5.  An  equilateral  triangular  flower  bed  has  an  area  of 
173  sq.  ft.    The  perimeter  is  60  ft.    What  is  the  altitude  ? 

6.  In  laying  out  a  triangular  flower  bed  the  sides  are 
all  made  equal,  and  the  perimeter  is  found  to  be   30  ft. 
and  the  altitude  8.6  ft.    What  is  the  area  ? 

7.  The  four  sides  of  the  roof  of  a  church  spire  are  tri- 
angles, each  with  base  20  ft.  and  altitude  50  ft.    How  many 
square  feet  in  each  triangle  ?    in  the  whole  roof  ? 

8.  A  man  buys  a  3-acre  lot  that  is  a  parallelogram  in 
shape.    The  frontage  along  the  road  is  100  rd.    What  is 
the  distance  to  the  rear  line  ? 

9.  For  the  panels  of  a  staircase  20  marble  slabs  are 
needed.  They  are  parallelograms,  each  with  a  base  1  ft.  6  in. 
and  an  altitude  4  ft.    What  is  the  area  of  all  the  slabs  ? 

10.  A  marble  floor  is  made  of  1000  equilateral  triangles, 
each  with  base  10  in.  and  altitude  8.6  in.    What  is  the  area 
of  the  floor  space  in  square  inches  ? 

11.  A  corner  lot,  where  two  streets  do  not  meet  at  right 
angles,  is  a  parallelogram  in  shape.    Its  length  along  one 
street  is  60  ft.,  and  the  distance  from  that  front  to  the  side 
parallel  to  it  is  100  ft.    What  is  its  area  ? 

12.  A  triangle,  a  square,  a  rectangle,  and  a  parallelogram 
all  have  the  same  base  and  the  same  altitude.    The  side  of 
the  square  is  4  in.    What  is  the  area  of  each  ? 


132  MEASURES 

40.  Rectangular  Solids 

Find  the  volumes  of  solids  of  the  following  dimensions : 

1.  2"  x  3"  x  4".  9.  3"  x  5"  x  6". 

2.  2"  x  4"  x  5".  10.  3"  x  6"  x  7". 

3.  2"  x  5"  x  6".  11.  4'  x  5'  x  10'. 

4.  2"  x  6"  x  7".  12.  4'  x  6'  x  10'. 

5.  2"x7"x8".  13.  5'x6'xll'. 

6.  2"  x  8"  x  9".  14.  5'  x  6'  x  12'. 

7.  3  rd.  x  4  rd.  x  5  rd.  15.  5  yd.  x  7  yd.  x  10  yd. 

8.  3  rd.  x  4  rd.  x  6  rd.  1  16.  6  yd.  x  7  yd.  x  11  yd. 

17.  At  50/  a  cubic  yard,  how  much  will  it  cost  to  exca- 
vate a  cellar  containing  320  cu.  yd.  ? 

18.  At  $2.25  a  cubic  yard,  how  much  will  it  cost  to  dig  a 
trench  3  ft.  deep,  18  in.  wide,  and  20  yd.  long  ? 

41.  Rectangular  Solids 

Given  the  following  volumes  of  boxes,  and  the  breadths  and 
lengths,  find  the  depths : 

1.  40  cu.  in. ;  2  in.,  4  in.  6.  60  cu.  in. ;  3  in.,  5  in. 

2.  90  cu.  in. ;  5  in.,  6  in.  7.  240  cu.  in. ;  4  in.,  6  in. 

3.  42  cu.  in. ;  3  in.,  7  in.  8.  120  cu.  in. ;  5  in.,  6  in. 

4.  72  cu.  in. ;  4  in.,  9  in.  9.  160  cu.  in. ;  5  in.,  8  in. 

5.  90  cu.  in. ;  5  in.,  6  in.  10.  180  cu.  in.  ;  4  in.,  5  in. 

11.  If  a  box  contains  54  cu.  in.,  and  the  area  of  the  base 
is  27  sq.  in.,  what  is  the  depth  ? 

12.  If  a  box  contains  72  cu.  in.,  and  the  depth  is  3  in., 
what  is  the  area  of  the  base  ? 

13.  If  a  box  contains  84  cu.  ft.,  and  the  length  is  7  ft. 
and  the  width  4  ft.,  what  is  the  depth  ? 

14.  If  a  box  contains  81  cu.  in.  and  the  base  contains 
27  sq.  in.,  how  deep  is  it  ?  ^ 


RECTANGULAR  SOLIDS  133 

42.   Rectangular  Solids 

1.  How  many  cubic  feet  in  a  bin  3'  x  4'  x  6'? 

2.  How  many  cubic  feet  in  a  room  15'  x  20'  x  10'? 

3.  How  many  cubic  inches  in  an  aquarium  5"  x  8"  x  12"  ? 

4.  Allowing  231  cu.  in.  to  a  gallon,  how  many  quarts  of 
water  will  an  aquarium  3"  x  7"  x  11"  contain  ? 

5.  Suppose  the  aquarium  described  in  Ex.  4  was  twice 
as  wide,  twice  as  deep,  and  twice  as  long,  how  many  quarts 
would  it  then  hold  ? 

6.  If  water  weighs  62^  Ib.  per  cubic  foot,  what  will  be 
the  weight  of  the  water  that  fills  a  rectangular  tank  5  ft. 
long,  2  ft.  wide,  and  1  ft.  deep  ? 

7.  A  tank  can  be  so  placed  in  a  house  that  its  base  has 
24  sq.  ft.    How  high  must  it  be  made  that  it  may  contain 
96  cu.  ft.? 

8.  A  bin  is  8  ft.  long  and  5  ft.  wide.    How  deep  must 
the  grain  be  in  order  that  there  shall  be  120  cu.  ft.?    160 
cu.  ft.  ?    140  cu.  ft.  ? 

9.  How  many  bars  of  soap,  each  2"  x  3"  x  4",  can  be 
packed  in  a  box  8"xl2"xl6"?    (In  such  cases  always 
cancel  mentally  before  multiplying.) 

10.  Allowing  550  cu.  ft.  of  clover  hay  to  the  ton,  how 
many  tons  will  it  take  to  fill  a  space  10'  x  10'  x  11'? 

11.  A  schoolroom  is  40  ft.  long,  20  ft.  wide,  and  10  ft. 
high.    How  many  cubic  feet  of  air  must  be  changed  per 
minute  in  order  to  change  it  all  in  20  min.  ? 

12.  A  schoolroom  is  50  ft.  long,  40  ft.  wide,  and  15  ft. 
high.    How  many  cubic  feet  does  it  contain  ? 

13.  A  schoolroom  is  40  ft.  wide  and  1^  times  as  long  as 
it  is  wide.    What  is  the  floor  area  ?    If  the  room  is  20  ft. 
high,  what  is  its  volume  ? 

14.  A  schoolroom  has  a  capacity  of  18,000  cu.  ft.    It  is 
15  ft.  high.    What  is  the  floor  area  ? 


134  MEASURES 

43.   Review 

1.  A  dealer  has  2  gal.  of  cream  that  he  sells  at  10/  per 
half  pint.    How  much  does  he  receive  ? 

2.  Allowing  6  plates  of  ice  cream  to  a  quart,  how  many 
gallons  should  be  allowed  for  48  persons  ? 

3.  Hogsheads  vary  in  size,  but  allowing  63  gal.  to  a 
hogshead,  how  many  quarts  does  it  contain  ? 

4.  A  man  has  a  10-quart  pail.    How  many  pailfuls  of 
water  must  he  take  to  fill  a  30-gallon  barrel  ? 

5.  Allowing  4|  cu.  ft.  to  a  barrel,  how  many  barrels  of 
water  will  a  cistern  of  29  cu.  ft.  contain  ?    of  58  cu.  ft.  ? 

6.  Allowing  7^  gal.  to  a  cubic  foot,  how  many  gallons 
of  water  will  a  cistern  of  100  cu.  ft.  contain  ? 

7.  Allowing  500  cu.  ft.  to  a  ton  of  hay,  how  many  tons 
will  it  take  to  fill  a  haymow  60  ft.  by  30  ft.  by  10  ft.? 

8.  How  many  loads   (cubic  yards)   of  earth   must  be 
removed  in  digging  a  cellar  21  ft.  by  30  ft.  by  6  ft.? 

9.  If  a  man  has  a  piece  of  meadow  land  80  rd.  long  and 
20  rd.  wide,  how  many  acres  does  it  contain  ? 

10.  Allowing  3l£  gal.  to  a  barrel,  how  many  gallons  in 
4  bbl.  ? 

11.  Allowing  24|   cu.  ft.  to  a  perch  of  masonry,  how 
many  cubic  feet  in  4  perches  ? 

12.  If  it  takes  35  cu.  ft.  of  a  certain  kind  of  hard  coal  to 
weigh  a  ton,  how  many  cubic  feet  in  5  tons  ?   How  many 
cubic  feet  in  20  tons  ? 

13.  Allowing  22  bricks,  including  the  mortar,  to  a  cubic 
foot,  how  many  bricks  are  there  in  a  brick  wall  that  con- 
tains 300  cu.  ft.  ? 

14.  A  boy  has  an  aquarium  that  contains  1728  cu.  in. 
Allowing  7£  gal.  to  a  cubic  foot,  how  many  gallons  of  water 
will  it  hold?    Suppose  he  had  one  containing  864  cu.  in., 
how  many  gallons  would  that  hold  ? 


LONGITUDE  AND  TIME  135 

III.   LONGITUDE  AND  TIME 

44.  Longitude  to  Time 

Given  the  following  differences  in  longitude,  find  the  cor- 
responding differences  in  local  time : 

1.  1°.  6.  2'.  11.  7".  16.  90°. 

2.  1'.  7.  2".  12.  45°.  17.  75°. 

3.  1".  8.  30°.  13.  7£°.  18.  105°. 

4.  15°.  9.  5°.  14.  15'.  19.  120°. 

5.  2°.  10.  6'.  15.  15".  20.  180°. 

21.  Two  ships  are  20°  of  longitude  apart.    What  is  the 
difference  in  time  ? 

22.  A  lighthouse  in  15°  W.  telegraphs  at  9  A.M.,  on  a 
direct  wire  to  Greenwich,  the  sighting  of  a  ship.    At  what 
time  does  the  message  reach  Greenwich  ? 

45.  Time  to  Longitude 

Given  the  following  differences  in  local  time,  find  the  cor' 
responding  differences  in  longitude : 


1. 

1  hr. 

6. 

8  min. 

11. 

20  min. 

16. 

H  hr. 

2. 

4  min. 

7. 

16  min. 

12. 

40  min. 

17. 

6hr. 

3. 

1  min. 

8. 

32  min. 

13. 

4  hr. 

18. 

7  hr. 

4. 

30  min. 

9. 

3hr. 

14. 

5hr. 

19. 

8  hr. 

5. 

2hr. 

10. 

2  min. 

15. 

30  min. 

20. 

12  hr. 

21.  When  it  is  noon  at  Greenwich,  where  is  it  midnight  ? 
In  what  part  of  the  world  is  it  forenoon  ?    In  what  part  of 
the  world  is  it  afternoon  ? 

22.  When  it  is  noon  at  Greenwich,  where  is  it  11  A.M.? 

1  P.M.  ?    2  P.M.  ?    3  P.M.  ?    6  P.M.  ? 

23.  When  it  is  noon,  local  time,  at  our  school,  how  many 
degrees  from  here,  and  in  which  direction,  is  it  10  A.M., 
local  time  ? 


136 


LONGITUDE  AND  TIME 


PACIFIC  TIME  120°  W.       MOUNTAIN  TIME  1  05°  W.       CENTRAL  TIME  90°  W.       EASTERN  TIME  75°  W. 


46.    Standard  Time 

1.  When  it  is  10  A.M.  by  Eastern  Time,  what  is  it  by 
Central  Time  ?    by  Mountain  Time  ?    by  Pacific  Time  ? 

2.  When  it  is  2  P.M.  by  Central  Time,  what  is  it  by  East- 
ern Time  ?   by  Mountain  Time  ?   by  Pacific  Time  ? 

3.  When  it  is  noon  by  Mountain  Time,  what  is  it  by 
Eastern  Time  ?    by  Central  Time?    by  Pacific  Time  ? 

4.  When  it  is  midnight  by  Pacific  Time,  what  is  it  by 
Eastern  Time  ?    by  Central  Time  ?   by  Mountain  Time  ? 

5.  When  it  is  1  P.M.  by  Eastern  Time,  what  is  it  by  Cen- 
tral Time  ?    by  Mountain  Time  ?   by  Pacific  Time  ? 

6.  When  it  is  6  P.M.  by  Central  Time,  what  is  it  by 
Pacific  Time  ?    by  Eastern  Time  ?   by  Mountain  Time  ? 

7.  When  you  begin  school  in  the  morning  what  time 
is  it  in  each  of  the  other  Standard  Time  sections  of  this 
country  ? 

8.  When  it  is  noon  at  Greenwich,  what  is  it  by  Eastern 
Time  ?   by  Central  Time  ?  by  Mountain  Time  ?   by  Pacific 
Time? 


STANDARD  TIME  137 

47.   Standard  Time 

1.  When  it  is  9  A.M.  in  New  York,  what  time  is  it  in 
Wisconsin  ?    in  Missouri  ?    in  Wyoming  ? 

2.  When  it  is  6  A.M.  in  Alabama,  what  time  is  it  in 
Louisiana  ?    in  Arkansas  ?    in  Colorado  ?    in  Delaware  ? 

3.  When  it  is  midnight  in  Utah,  what  time  is  it  in  Cali- 
fornia ?    in  Iowa  ?    in  Mississippi  ?    in  Maryland  ? 

4.  When  it  is  noon  in  Michigan,  what  time  is  it  in 
Memphis  ?    in  New  Orleans  ?    in  eastern  Texas  ?    in  west- 
ern Oregon  ? 

5.  When  it  is  2  P.M.  in  Massachusetts,  what  time  is  it  in 
Maine  ?    in  Vermont  ?    in  Lincoln,  Nebraska  ?    in  Guthrie, 
Oklahoma  ?    in  Seattle  ? 

6.  When  it  is  7  P.M.  in  Florida,  what  time  is  it  in  New 
Hampshire?   in  Connecticut?   in  Savannah?   in  Louisville? 

7.  When  it  is  8.30  A.M.  in  Butte,  what  time  is  it  in 
Chicago  ?    in  Cleveland  ?    in  Portland,  Oregon  ?    in  Port- 
land, Maine  ? 

8.  When  it  is  midnight  in  Greenwich,  England,  what 
time  is  it  in  New  York  ?    in  Chicago  ?    in  Denver  ?    in  San 
Francisco  ?    where  you  live  (by  Standard  Time)  ? 

9.  What  time  is  it  now  in  your  school  ?    in  Ehode  Is- 
land ?    in  Cincinnati  ?    in  New  Orleans  ?    in  Galveston  ?    in 
Salt  Lake  City  ?    in  Los  Angeles  ? 

10.  Great    Britain   uses    Greenwich    time    and    Central 
Europe  uses  that  of  15°  E.    When  it  is  noon  in  London, 
what  time  is  it  in  Berlin  ?    in  Milwaukee  ? 

11.  When  it  is  noon  in  Venice  (15°  E.),  what  time  is  it  in 
Edinburgh  ?    in  Munich  ?    in  London  ?    in  Berlin  ?    where 
you  live  ? 

12.  When  you  go  away  from  school  in  the  afternoon 
(Standard  Time),  what  time  is  it  in  Greenwich,  England  ? 
in  Central  Europe  ? 


138  PERCENTAGE 

IV.  PERCENTAGE 

48.  Expressing  Per  Cents 

To  express  £  as  per  cent,  think  of  it  as  -f6°^  and  say  "  50  per  cent." 
We  may  read  1.50  as  "1  and  50  hundredths,"  "150  hundredths," 
or  "150  per  cent." 

Express  as  per  cents  : 

1.  TVo-  5..  .75.  9.  .12^.  13.  1.25.  17.  .66$. 

2.  .25.  6.  .20.  10.  .33$.  14.  1.50.  18.  3.20. 

3.  £.  7.  |.  11.  .16|.  15.  2.75.  19.  4.75. 

4.  f.  8.  .12.  12.  .061.  16.  0.99.  20.  5.50. 

21.  A  man  loans  some  money  and  receives  ^  of  the 
amount  each  year  as  interest.    What  per  cent  is  this  ? 

22.  Some  damaged  goods  are  sold  at  ^  less  than  they 
cost.    This  is  what  per  cent  less  than  they  cost  ? 

49.  Expressing  Per  Cents 

Express  as  per  cents : 

1.  \.  5.  If.  9.  l\.  13.  f.    !          17.  TV 

2.  i.  6.  \.  10.  1|,1SJ*/  14.  If.  18.  ,V 

3.  f.    '         7.  f.3         11.  J.-V*       15.  If.  19.  12V 

4.  1J.  8.  f.^'v    12.  f.  *4*      16.  T%V          20.  1^. 

21.  A  quart  is  what  part  of  a  gallon  ?   what  per  cent  of 
a  gallon  ? 

22.  If  i  of  a  farm  is  wooded,  and  \  of  this  is  a  grove  of 
pine  trees,  what  per  cent  of  the  farm  is  this  grove  ? 

23.  If  \  of  the  pupils  in  a  school  are  boys,  and  ^  of 
these  are  in  the  sixth  grade,  the  boys  in  the  sixth  grade 
are  what  per  cent  of  all  the  pupils  in  the  school  ? 

24.  If  a  boy  picks  300  apples  and  sells  150  of  them,  what 
per  cent  does  he  sell  ?   What  per  cent  has  he  left  ? 


\  PER  CENTS  AS  FRACTIONS  139 

/ 

50.   Per  Cents  as  Fractions 

, 

To  express  75%  as  a  common  fraction,  think  of  it  as  T7557  reduced 
to  lowest  terms,  or  £. 

Express  as  common  fractions  : 

1.  10%.       3.  25%.      5.  40%.       7.  60%.        9.  80%.        | 

2.  20%.       4.  30%.      6.  45%.      8.  85%.       10.  125%.  /  ^ 

11.  Which  is  the  greater,  20%  or  £  ?    25%  or  £  ?    50% 
or  i? 

Learn  the  following  important  per  cents  : 


12.  50%  =  $. 
13.  25%  =|. 
14.  12$%  =  i- 

16.  33^%  =  $. 
17.  66f%=§. 
18.  16f%  =  $. 
19.  8^%  =  ^V 

20.  20%  =  $. 
21.  37^%  =  |. 
22.  62^%  *  f. 
23.  87^%  =  |. 

51.   Per  Cents  as  Fractions 

Express  as  common  fractions  or  mixed  numbers : 

1.  35%.  5.  1.25.  9.  .32.  13.  60%.  17. 

2.  .35.  6.  75%.  10.  2.20.  14.  .60.-  18.  66f%. 

3.  24%.  7.  .75.  11.  40%.  15.  3.60.  19.  37i%. 

4.  .24.  8.  32%.  12.  .40.  16.  12J%.  20.  137$%. 

21.  "What  is  a  short  way  of  finding  12 $%  of  a  number  ? 
What  is  12^%  of  88  ?     ^L' 

22.  What  is  a  short  way  of  finding  37|%  of  a  number? 
What  is  37^%  of  88? 

23.  What  is  a  short  way  of  finding  87^%  of  a  number? 
What  is  87^%  of  16? 

24.  Express  125%  in  three  other  ways.    You  might  use 
hundredths,  or  an  improper  common  fraction,  or  a  mixed 
number,  or  a  mixed  decimal. 


140  PERCENTAGE 

52.   Per  Cents  of  Numbers 

Think  of  50%  as  |,  25%  as  £,  12  \%  as  \.   This  makes  the  finding  of 
these  per  cents  much  more  simple. 

Find  the  values  of  the  following  : 


1.  50%  of  36.  7.  25%  of  20.         13.  12%%  of  8. 

2.  50%  of  48.  8.  25%  of  48.         14.  12^%  of  32. 

3.  50%  of  120.         9.  25%  of  100.       15.  12$%  of  48. 

4.  50%  of  25.  '        10.  25%  of  5.  16.  12$%  of  64. 

5.  50%  of  $6.*     11.  25%  of  21.         17.  12$%  of  72. 

6.  50%  of  500.       12.  25%  of  240.       18.  12$%  of  160. 

19.  In  a  box  of  200  oranges  25  %  are  "  blood  "  oranges. 
How  many  are  "  blood  "  oranges  ? 

20.  If  there  are  52  pupils  in  a  class  and  50%  are  boys, 
how  many  boys  are  there  ? 

53.   Per  Cents  of  Numbers 

Think  of  20%  as  $,  33|%  as  J,  66f%  as  |,  6J%  as  TV 
Find  the  values  of  the  following  : 
1.  20%  of  50;    •        7.  33  J%  of  15.         13.  6£%  of  16. 


2.  20%  of  35.           8.  33J  %  of  33.         14.  6J%  of  32. 

3.  20%  of  45.  9.  33J%  of  27.         15.  61%  of  160. 

4.  20%  of  75.         10.  33  J%  of  60.        16.  66§%  of  30. 

5.  20%  of  150.       11.  33J%  of  150.       17.  66§%  of  33. 

6.  20%  of  -$5.50.    12.  33J%  of  $3.30.    18.  66f  %  of  $60. 
19.  20%  of  25%  of  400.  20.  33^%  of  50%  of  60. 

21.  If  20%  of  a  shipment  of  $500  of  freight  is  destroyed 
in  a  railway  accident,  what  is  the  value  of  the  freight 
destroyed  ? 

22.  If  33^%  of  a  man's  income  is  spent  for  rent  and 
clothes,  and  his  income  is  $90  a  month,  how  much  does  he 
spend  for  these  purposes  each  month  ? 


PER  CENTS  OF  NUMBERS  141 

54.  Per  Cents  of  Numbers 

Think  of  5%  of  200  as  5  x  1%  of  200,  or  5  x  2.   That  is,  first  find 
1%  of  the  number,  and  then  the  required  per  cent. 

Find  the  values  of  the  following : 

1.  1%  of  500.  5.  4%  of  300.  9.  9%  of  600. 

2.  2%  of  100.  6.  6%  of  200.  10.  1%  of  250. 

3.  2%  of  200.  7.  7%  of  300.  11.  2%  of  250. 

4.  3%  of  200.  8.  8%  of  400.  12.  3%  of  110. 

13.  A  dealer  bought  $300  worth  of  goods,  but  by  prompt 
payment  was  allowed  to  have  them  for  5%  less.    How  much- 
did  he  gain  in  this  way  ? 

14.  An  orchard  that  produced  600  bu.  of  apples  last  year 
produced   8%    more   this  year.     What   was    the   gain   in 

bushels  ?    What  was  the  number  of  bushels  this  year  ? 

r 

55.  Per  Cents  of  Numbers 

1.  1%  of  600.  7.  10%  of  70.  13.  25%  of  400. 

2.  2%  of  700.  8.  20%  of  65.  14.  25%  of  72. 

3.  5%  of  900.           9.  20%  of  85.  15.  25%  of  500. 

4.  8%  of  500.  10.  20%  of  155.  16.  50%  of  700. 

5.  9%  of  400.  11.  20%  of  75.  17.  50%  of  900. 

6.  6%  of  $40.  12.  20%  of  305.  18.  75%  of  480. 

19.  How  much  is  25%  profit  on  goods  that  cost  $2400  ? 

20.  How  much  is  6%   loss  on  goods  that  cost  $700  ? 
on  goods  that  cost  $1200  ? 

21.  How  much  is  10%  discount  on  $1650  worth  of  goods  ? 
on  $2775  worth  of  goods  ? 

22.  How  much  is  75%  fire  loss  on  property  valued  at 
$3200  ? 

23.  If  some  goods  are  marked  at  $800,  and  a  dealer  sells 
them  for  12^%  less,  for  how  much  less  does  he  sell  them  ? 


142  PERCENTAGE 

56.   Per  Cents  of  Numbers 

1.  12i%  Of  16.  e.  33^%  of  249.  11.  16|%  of  72. 

2.  12^%  of  72.  7.  66f  %  of  12.  12.  16f  %  of  300. 

3.  12^%  of  168.  8.  66f  %  of  33.  13.  37£%  of  16. 

4.  33 \%  of  15.  9.  66f  %  of  150.  14.  37£%  of  40. 

5.  33 J%  of  42.  10.  16f%  of  18.  15.  62^%  of  800. 

16.  A  merchant  did  $16,000  worth  of  business  one  year 
and  12£%   more  the  next  year.    Express  the  increase  in 
dollars. 

17.  A  school  that  had  an  enrollment  of  320  last  year  has 
an   enrollment  6|%   greater  this  year.    How  many  more 
pupils  has  it  now? 

18.  A  cattle  dealer  bought  some  cattle  for  $2700  and 
after  fattening  them  he  sold  them  for  33 \°f0  more  than  he 
paid.    What  was  the  selling  price  ? 

57.   Finding  the  Rate 

To  find  what  per  cent  24  is  of  400,  think  of  it  as  -gfo  of  400,  or  Tf  ff 
of  it,  or  6%.   The  per  cent  is  then  6,  or  the  rate  is  6%. 

Find  what  per  cent  the  first  number  is  of  the  second: 

.     1.  7,  100.  ^  5.  10,  200.  9.  24,  300. 

2.  16,  100.  6.  16,  200.  10.  $8,  $400. 

3.  33£,  100.  /  7.  6,  300.  11.  15  ft.,  500  ft. 
.^  4.  6,  200.  /<*.  12  ft.,  ,300  ft.  12.  63  in.,  900  in. 

13.  How  much  is  a  year's  interest  on  $1000  at  6%  ? 

14.  If  you  miss  1  question  out  of  25,  what  per  cent  do 
you  miss  ? 

i  ^  15.  If  you  lose  5  ft.  from  50  ft.  of  fishing  line,  what  per 

~~cent  do  you  lose  ? 

\/    16.  If  a  merchant  gains  $30  by  selling  $300  worth  of 
/  ^Dods,  what  is  his  per  cent  of  gain  ? 

\ 


PER  CENTS  143 

58.   Finding  Per  Cents 

1.  H  is  what  part  as  large  as  G  in  this  picture  ? 

2.  Then  H  is  what  part  of  G  ?    G  is  what  part  of  E  ? 

3.  G  is  how  many  times  as  large 
as  H?    Then  what  per  cent  is  G  of  H? 

4.  H  is  what  part  as  large  as  jF? 
what  per  cent  of  .F?    F  is  what  per 

cent  of  H?  \~ 

5.  H  is  what  part  as  large  as  E  ?        . — I 

what  per  cent  of  E  ?    E  is  what  per    p J — ; 

cent  of  H? 


Tell  the  relation  by  a  fraction  or  integer,  and  then  the  per 
cent  relation  of: 

6.  G  to  E.  11.  FtoE.  16.  C  to  E. 

7.  £  to  A.  12.  #  to  F.  17.  C  to  A 

8.  H  to  ^.  13.  E  to  ZX  18.  G  to  A. 

9.  G  to  F.  14.  Z>  to  £.  19.  F  to  C. 
10.  .F  to  G.  15.  E  to  C.  20.  C  to  .F. 

21.  If  A  in  the  picture  represents  $1000,  which  one  of 
the  rectangles  represents  50%  of  it  ?    How  much  is  this  ? 

22.  If  E  in  the  picture  represents  $400,  which  one  of 
the  rectangles  represents  25%  of  it?    How  much  is  this? 

23.  If  .Pin  the  picture  represents  $600,  which  one  of  the 
rectangles  represents  66f%  of  it  ?    How  much  is  this  ? 

24.  If   A    in    the   picture    represents   $800,  which    one 
of   the    rectangles    represents    12^%   of   it  ?    How   much 
is  this  ?    How  much  is  25%  of  it  ?    50%  ? 

25.  If  H  in  the  picture  represents  $500,  which  one  of 
the  rectangles  represents  200%  of  it?    How  much  is  this? 

26.  If  E  in  the  picture  represents  40  tons,  which  one  of 
the  rectangles  represents  125%  of  it?    Which  one  repre- 
sents 150%  of  it  ? 


144 


PERCENTAGE 


59.   Per  Cents  of  Numbers 
Find  125  °f0  of  (or  _?|  times)  the  following  : 

$160.  7.  72  ft. 

8.  $360. 


1.  36. 

2.  64. 

3.  80ft. 


4. 

5.  28. 

6.  32. 


9.  80. 


10.  88. 

11.  60ft. 

12.  $2.40. 


Find  150  cfo  of  the  following  : 

13.  40.  16.  $220.  19.  90yd.         22.  52. 

14.  30.  17.  70.  20.  $150.  23.  62  rd. 

15.  60  in.          18.  25.  21.  38.  24.  $1.20. 

25.  If  a  man  sells  $2400  worth  of  goods  at  25%  profit, 
what  is  the  selling  price  ? 

26.  If  a  manufacturer  spent  $50,000  in  advertising  and 
increased  this  50%,  how  much  did  he  then  spend  ? 

60.   Per  Cents  of  Numbers 
Find  133~^0  of  the  following  : 


1.  36. 

2.  48. 


3.  60  A. 

4.  $150. 


5.  51. 

6.  57. 


Find  116  '|%>  of  the  following  : 

9.  36.  11.  30  yd.          13.  54. 

10.  48.  12.  $360.  14.  72. 


7.  90  min. 

8.  $2.70. 


15.  84  rd. 

16.  $2.40. 


Find  112%  °/o  of  the  following  : 

17.  32.  19.  56ft.  21.  72.  23.  88yd. 

18.  48.  20.  $640.  22.  96.  24.  $1.44. 

25.  Goods  costing  $2400  are  sold  at  16§%  above  cost. 
What  is  the  selling  price  ? 

26.  Goods  coating  $2700  are  damaged  to  the  extent  of 

What  is  the  loss  ? 


PER  CENTS  145 

61.   Review 

1.  In  a  school  of  300  pupils  9%  were  in  the  seventh 
grade.    How  many  were  in  that  grade  ? 

2.  In  a  school  of  200  pupils  11%  were  in  the  third  grade 
and  14%  were  in  the  first  grade.    How  many  were  in  each 
of  these  grades  ? 

3.  Of  300  pupils,  5%  have  been  tardy  or  absent  this 
month.    How  many  have  not  been  tardy  or  absent  ? 

4.  In  a  school  of  300  pupils,  if  there  should  be  an  in- 
crease of  3^%  next  year,  how  many  pupils  would  there 
then  be  ? 

5.  In  a  school  of  250  pupils  there  were  10%  less  pupils 
four  years  ago.    How  many  were  there  then  ? 

6.  If  16§%  of  the  pupils  in  a  school  of  240  pupils  were 
not  in  the  school  last  year,  how  many  new  ones  are  'there 
this  year  ? 

./  7.  If  20%  of  the  pupils  in  a  school  of  250  pupils  are 
in  the  seventh  and  eighth  grades,  how  many  are  in  those 
grades  ? 

8.  If  25%  of  the  pupils  of  a  school  of  300  pupils  are  in 
the  first  and  second  grades,  how  many  are  in  those  grades  ? 
in  all  the  other  grades  ? 

9.  If  55%  of  the  pupils  in  a  school  of  300  pupils  are 
girls,  how  many  girls  in  the  school  ?    How  many  boys  ? 

10.  What  must  be  added  to  250  ft.  to  increase  it  50%  ? 
to  increase  it  100%  ? 

11.  What  must  be  added  to  240  Ib.  to  make  it  125%  of 
the  present  weight  ? 

12.  A  column  of  mercury  in  a  thermometer  is  6  in.  high. 
If  it  increases  16§%  in  height,  how  high  is  it  ? 

13.  A  rectangle  4  in.  long  and  3  in.  wide  is  increased 
50%  in  length  and  33^%  in  width.    What  was  the  original 
area  and  what  is  the  area  now  ? 


146  PERCENTAGE 

62.  Finding  the  Rate 

To  find  what  per  cent  15  is  of  25,  think  of  ^f  of  25,  or  T%%  of  25, 
and  state  the  result,  60%. 

Find  what  per  cent  the  first  number  is  of  the  second : 

1.  5,  10.  6.  40,  200.  11.  11,  50. 

2.  10,  20.  7.  7,  20.  12.  150,  50. 

3.  50,  100.  8.  9,  20.  13.  $2,  $10. 

4.  6,  25.  9.  15,  300.  14.  3  ft.,  20  ft. 

5.  7,  25.  10.  9,  50.  15.  $30,  $50. 

16.  A  man's  income  is  $1000  a  year  and  he  saves  $250. 
What  per  cent  does  he  save  ? 

17.  A  man's  income  is  $1500  a  year  and  he  saves  $600. 
What  per  cent  does  he  save  ?  (Tfi5  =  how  many  fifths  ?  then 
how  many  hundred ths  ?) 

63.  Finding  the  Rate 

1.  2  is  what  part  of  4  ?    what  per  cent  of  4  ? 

2.  3  is  what  part  of  12  ?    what  per  cent  of  12  ? 

3.  5  is  what  part  of  40  ?   what  per  cent  of  40  ? 

4.  7  is  what  part  of  21  ?    what  per  cent  of  21  ? 

5.  9  is  what  part  of  45  ?    what  per  cent  of  45  ? 

find  what  per  cent  the  first  number  is  of  the  second: 

6.  30,  60.  "^      9.  15,  45.#jl2.  12,  96.        15.  50,  25. 

7.  20,  80.  v*  10.  30,  45^6^13.  16,  40.        16.  25,  20. 

8.  12,  60.        11.  66,  88.7yl4.  72,  72.       17.  52,  156. 

18.  An  income  of  $400  on  $8000  is  what  per  cent  ? 

19.  If  a  man  gains  $600  on  an  investment  of  $12,000, 
what  is  his  rate  of  gain  ? 

20.  If  a  dealer  loses  $200  on  goods  that  cost  $1200,  what 
is  his  per  cent  of  loss  ? 


FINDING  THE  RATE  147 

64.  Finding  the  Rate 

Find  what  per  cent  the  first  of  these  numbers  is  greater 
than  the  second  : 

1.  60,  40.          3.  60,  48.          5.  88,  66.          7.  63,  56. 

2.  54,  36.          4.  75,  60.          6.  64,  48.          8.  110,  66. 

Find  what  per  cent  the  first  of  these  numbers  is  less  than 
the  second: 

9.  35,  70.        11.  50,  75.        13.  54,  60.        15.  25,  40. 
10.  48,  64.        12.  42,  48.        14.  56,  70.        16.  100,  150. 

Find  what  per  cent  the  first  of  these  numbers  is  greater 
than  the  second ;  the  second  what  per  cent  less  than  the 
first  : 

17.  15,  10.        18.  25,  20.        19.  40,  30.        20.  75,  25. 

65.  Finding  the  Base 

To  find  of  what  number  25  is  5%,  think  that  if  5%  of  the  number  is 
25,  1%  of  it  is  5,  and  100%  of  the  number  is  500.  Or  25  may  be  thought 
of  as  ^  of  the  number  ;  hence  the  number  is  20  x  25,  or  500. 

Find  the  numbers  of  which  the  following  are  the  given 
per  cents  : 

1.  30,  6%.  5.  35,  7%.  9.  $20,  4%. 

2.  36,  6%.  6.  49,  7%.  10.  $50,  5%. 

3.  35,  5%.  7.  50,  25%.  11.  $63,  7%. 

4.  45,  o%.  8.  75,  25%.  12.  250  ft.,  25%. 

13.  Some  men  at  work  in  a  ditch  have  dug  24  ft.  of  it 
to-day,  which  is  8%  of  the  total  length.    What  is  the  total 
length  ? 

14.  A  school  has  20%  of  its  pupils  in  the  sixth  grade, 
which  numbers  40.    How  many  pupils  in  the  school  ?    How 
many  pupils  in  grades  other  than  the  sixth  ? 


148  PERCENTAGE 

66.   Review 

1.  If  a  man  loans  $250  and  receives  $10  interest  for  a 
year,  what  is  the  rate  ? 

2.  If  a  man  borrows  $300  and  pays  $18  interest  for  a 
year,  what  is  the  rate  ? 

3.  If  a  salesman  receives  a  commission  of  $15  on  a  sale 
amounting  to  $750,  what  is  his  rate  of  commission  ? 

4.  If  a  dairyman  keeps  60  cattle  this  year  and  kept  48 
last  year,  what  is  the  increase  per  cent  ? 

5.  If  the  taxes  of  a  certain  village  were  $8000  last  year 
and  $7000  this  year,  what  is  the  decrease  per  cent  ? 

6.  If  the  rainfall  in  a  certain  place  was  7.2  in.  in  April 
and  6  in.  in  March,  what  was  the  per  cent  of  increase  ? 

7.  If  the  seventh  grade  devotes  45  min.  a  day  to  arith- 
metic and  the  sixth  grade  40  min.,  what  is  the  per  cent  of 
increase? 

8.  If  a  dealer  sold  daily  150  qt.  of  milk  last  month  and 
180  qt.  this  month,  what  was  the  rate  of  increase  ? 

9.  If  a  class  had  25  examples  on  Monday  and  28  on 
Tuesday,  what  was  the  rate  of  increase  ? 

10.  If  you  have  read  75  pages  in  a  book  of  300  pages, 
what  per  cent  have  you  read  ? 

11.  If  the  last  chapter  of  a  book  is  numbered  XXXII 
and  you  have  finished  Chapter  XXIV,  what  per  cent  of  the 
chapters  have  you  read  ? 

12.  If  you  have  read  60  pages  of  a  book,  and  this  is  25% 
of  the 'book,  how  many  pages  are  there  in  all  ?    How  many 
pages  have  you  still  to  read  ? 

13.  A  piece  of  cork  is  pushed  down  below  the  surface  of  a 
full  glass  of  water,  and  the  water  that  runs  over  is  weighed. 
The  cork  is  then  weighed  and  is  found  to  weigh  1.2  oz., 
while  the  water  weighed  5  oz.    Cork  is  what  per  cent  as 
heavy  as  an  equal  volume  of  water  ? 


FINDING  THE  BASE  149 

67.   Finding  the  Base 

To  find  of  what  number  9  is  25%,  think  of  9  as  \  of  it ;  therefore  £ 
of  it  is  4  x  9,  or  36.    Compare,  also,  Exercise  65. 

Find  the  numbers  of  which  the  following  are  the  given 
per  cents  : 

1.  4,  25%.  5.  6,  50%.  .  9.  25,  25%. 

2.  5,  25%.  6.  8,  50%.  10.  25,  10%. 

3.  7,  10%.  7.  8,  12^%.  11.  60,  50%. 

4.  9,  10%.  8.  7,  12£%.  12.  20,  12i%. 

13.  State  of  what  amount  $200  is  12£%. 

14.  The  width  of  a  brick  is  50%  of  its  length.   If  it  is 
4  in.  wide,  how  long  is  it  ? 

15.  The  thickness  of  a  brick  is  25%  of  its  length.    If  it  is 
2  in.  thick,  how  long  is  it  ? 


68.    Finding  the  Base 

Find  the  numbers  of  which  the  following  are  the  given 
per  cents : 

1.  4,  33^%.  4.  3,  20%.  7.  2,  5%. 

2.  7,  33J%.  5.  8,  20%.  8.  3,  5%. 

3.  12,  33^%.  6.  11,  20%.  9.  10,  5%. 

10.  The  thickness  of  a  board  is  12£%  of  its  width.    The 
board  is  1  in.  thick.    How  wide  is  it? 

11.  A  man  pays  33^%  of  a  mortgage  on  his  farm.    He 
pays  $1500.    How  much  was  the  mortgage  ? 

12.  If  a  dealer  sold  33^  %  of  his  stock  during  the  holidays, 
and  received  $2000,  what  was  the  selling  price  of  all  of  his 
stock  before  the  holidays  ? 

13.  If  20%  of  the  pupils  in  a  school  are  in  the  first  grade, 
and  there  are  40  in  that  grade,  how  many  pupils  are  there 
in  the  whole  school  ? 


150  PERCENTAGE 

69.  Finding  the  Base 

To  find  of  what  number  $30  is  150%,  think  that  1|  x  some  number 
is  $30  ;  so  the  number  is  §30  -^-  1£,  or  $30  -r-  f ,  or  f  of  $30,  or  $20. 

Find  the  number  represented  by  x  : 

1.  l£  times  x  is  9.  5.  150%  of  x  is  6. 

2.  1^  times  x  is  .10.  6.  125%  of  x  is  15. 

3.  If  times  x  is  14.  7.  175%  of  a;  is  21. 

4.  l£  times  x  is  12.  8.  120%  of  x  is  18. 
9.  133 £%  of  what  number  is  200  ? 

10.  If  you  have  50%  more  money  than  you  had  last  week, 
you  have  what  per  cent  as  much  as  you  had  then  ?    Suppose 
you  have  15/  now,  what  did  you  have  then  ? 

11.  If  a  man  has  125%   as  much  money  in  the  bank 
this  week  sfs  he  had  last  week,  and  has  $1250  now,  what 
did  he  have  then  ? 

70.  Finding  the  Base 

If  75%  of  some  number  is  60,  then  £  of  it  is  60,  J  of  it  is  20,  and 
|  of  it  is  80. 

Find  the  number  represented  by  x  : 

1.  i  of  x  is  7.  5.  25%  of  cc  is  9. 

2.  i  of  x  is  8.  6.  50%  of  x  is  13. 

3.  a  of  a;  is  12.  7.  75%  of  x  is  15. 

4.  f  of  x  is  24.  8.  80%  of  x  is  36. 
9.  If  I  take  20%  of  a  number,  what  per  cent  is  left  ? 

10.  After  decreasing  a  number  20%  there  remains  48. 
What  is  the  number  ? 

11.  After  decreasing  a  number  25%  there  remains  45. 
What  is  the  number  ? 

12.  After  drawing  out  10%  of  his  money  a  man  still  has 
in  the  bank.    How  much  had  he  at  first  ? 


FINDING  THE  BASE  151 

71.    Finding  the  Base 

1.  30  is  |  of  what  number  ?    50%  of  what  number  ? 

2.  30  is  £  of  what  number  ?    33^%  of  what  number  ? 

3.  30  is  ^  of  what  number  ?   25%  of  what  number? 

The  following  numbers  are  the  given  per  cents  of  what  other 
numbers  ? 


4.  7,  1%. 

9.  18,  6%. 

14.  33,  33J%. 

5.  8,  2%. 

10.  19,  10%. 

15.  22,  66f  %. 

6.  6,  3%. 

11.  21,  20%. 

16.  72,  50%. 

7.  8,  4%. 

12.  20,  12^%. 

17.  60,  75%. 

8.  15,  5%. 

13.  32,  25%. 

18.  16,  80%. 

19.  At  6%,  $18  is  the  interest  on  what  sum  for  a  year  ? 

20.  At  5%,  $60  is  the  interest  on  what  sum  for  a  year  ? 

21.  At  4%,  $40  is  the  interest  on  what  sum  for  a  year  ? 

72.   Finding  the  Base 

If  360  is  112^%  of  some  number,  360  is  f  of  it.    Hence  |  of  it  is  40, 
and  |  of  it  is  320. 

The  following  numbers  are  the  given  per  cents  of  what  other 
numbers  ? 

1.  $240,  150%.  5.  $180,  120%.  9.  450  ft.,  125%. 

2.  $200,  125%.  6.  $270,  112^%.  10.  9000  ft.,  75%. 

3.  $240, 133-^%.  7.  540ft.,112^%.  11.  3500  mi.,  50%. 

4.  $145,  200  % .  8.  420  ft,  120  % .  12.  1200  yd,,  33^  % . 

13.  A  boy  loses  60  ft.  of  his  kite  string,  which  is  20% 
of  it.    What  was  the  original  length  ? 

14.  A  man  spends  $900  of  his  income,  which  is  75%  of  it. 
What  is  his  income  ? 

15.  If  a  man  has  added  10%  to  the  size  of  his  farm 
and  now  has  220  acres,  how  much  did  he  have  at  first  ?  t 


152  PERCENTAGE 

73.   Discount 

Think  of  10%  discount  on  $75  as  ^  of  $75,  or  $7.50;  and,  in  general, 
use  common  fractions  for  mental  work  in  such  cases. 

Find  the  discotmts  on  the  following  amounts  at  the  rates 
specified : 

1.  $80,  10%.  5.  $40,  25%.  9.  $120,  10%. 

2.  $25,10%.  6.  $88,  25%.  10.  $150,  20%. 

3.  $50,  20%.  7.  $60,  50%.  11.  $160,  25%. 

4.  $25,  20%.  8.  $90,  50%.  12.  $250,  50%. 

13.  If  a  dealer  offers  me  an  80/  book  at  a  discount  of  25  % , 
this  is  how  many  cents  below  the  regular  price  ? 

14.  If  a  merchant  buys  $800  worth  of  goods,  and  is  allowed 
10%  discount  if  he  pays  for  them  at  once,  how  much  does 
he  gain  by  prompt  payment  ? 

74.   Net  Prices 

Think  of  $80  less  10%  discount  as  $80  -  $8,  or  $72. 
Find  the  amounts  remaining  after  deducting  the  discounts : 

1.  $60,  10%.  5.  $25,  20%.  9.  $80,  25%. 

2.  $50,  10%.  6.  $75,  20%.  10.  $40,  50%. 

3.  $70,  10%.  7.  $16,  25%.  11.  $70,  50%. 

4.  $50,  20%.  8.  $40,  25%.  12.  $120,  50%. 

13.  If  some  goods  are  marked  $20.  and  10%  discount  is 
allowed,  what  is  the  selling  price  ? 

14.  If  a  dealer  sells  some  goods  marked  $500  for  20%  less 
than  the  marked  price,  how  much  does  he  receive  ? 

15.  At  a  bargain  sale  a  set  of  furniture  marked  $44  is 
sold  at  25%  discount.    What  is  the  selling  price  ? 

16.  If  at  a  bargain  sale  a  fifteen-dollar  rug  is  offered  at 
20%  discount,  what  is  the  net  price  ? 


1 

DISCOUNT  1:53 

75.    Single  Discounts 

Think  of  33i  %  off  as  |  off.    If  goods  marked  $6  are  sold  at 
off,  the  net  price  is  $6  —  ^  of  $6,  or  §4. 

Given  the  marked  prices  and  rates  of  discount,  find  the 
net  prices : 

1.  $1,  10%.?°  07.  $4,  25%.  13.  $8,  12£%.  ' 

2.  $3,  10%.  1«  *8.  $8,  25%.     <P    14.  $4,  12£%.  3£ 


10%.     '      8.  $8,  25% 

3.  $7,10%.  U'%.  $24,25%.  }}   15.  $24,  12^%. 

4.  $1,20%.  .S'frlO.  $9,33^%.   V    16.  $12,50%.     (, 

5.  $5,  20%.  v, "'  11.  $6,  33J%.    M    17.  $20,  10%.    f< 

6.  $15,  20%.*-- 12.  $24,  33^%.  » V  18.  $25,  20%.    9  0* 

19.  How  much  is  $7.50  less  33^%  ? 

20.  If  goods  marked  $400  are  sold  to  a  dealer  at  a  dis- 
count of  20%,  what  do  they  cost  him  ? 

76.   Double  Discounts 

Think  of  $50  less  10  %,  10  %,  as  $50  less  10  %,  and  this  also  less  10%  ; 
or  as  §50  -  $5,  and  this  as  $45  -  $4.50,  leaving  $40.50. 

Given  the  marked  prices  and  rates  of  discount,  find  the 
net  prices  : 

1.  $1,  10%,  10%.  6.  $10,  10%,  10%. 

2.  $1,  20%,  10%.  7.  $20,  20%,  10%. 

3.  $1,  20%,  20%.  8.  $40,  20%,  20%. 

4.  $1,  20%,  25%.  9.  $80,  20%,  25%. 

5.  $1,  50%,  10%.  10.  $60,  50%,  20%. 

11.  If  goods  are  marked  $500  and  are  sold  to  a  dealer  at 
20%,  10%  discount,  what  do  they  cost  him  ? 

12.  What  is  the  net  price  of  goods  marked  $100  and  sold 
at  a  discount  of  20%,  20%  ?    Suppose,  instead,  they  had 
been  sold  at  a  discount  of  40%,  what  would  have  been  the 
net  price? 


154  PERCENTAGE 

77.  Profits 

Think  of  10%  more  than  $2.50  as  $2.50  +  $0.25,  or  §2.75. 
Add  the  following  per  cents  to  the  amounts  given : 

1.  $1,  10%.  6.  $20,  20%.  11.  $9,  3 

2.  $2,  10%.  7.  $1,  25%.  12.  $36,  33^%. 

3.  $6,  10%.          8.  $2,  25%.  13.  $4, 

4.  $1,  20%.  9.  $36,  25%.  14.  $2,  12 

5.  $2,  20%.  10.  $3,  33£%.  15.  $80, 

16.  A  merchant  pays  $75  for  some  goods  and  sells  them 
at  a  profit  of  20%.    What  is  the  selling  price  ? 

17.  A  merchant  buys  some  goods  for  $400  and  sells  them 
at  a  profit  of  25%.    What  is  the  selling  price  ? 

18.  A  merchant  buys  $2000  worth  of  goods  and  sells 
them  at  125%  of  their  cost.    What  is  the  selling  price  ? 

78.  Losses 

Subtract  the  following  per  cents  from  the  amounts  given  : 

1.  $5,  10%.  5.  $4,  20%.  9.  $20,  20%. 

2.  $9,  10%.  6.  $3,  25%.  10.  $40,  25%. 

3.  $8,  10%.  7.  $5,  25%.  11.  $12, 

4.  $5,  20%.  8.  $6,  50%.  12.  $40, 

13.  Some  goods  costing  $90  were  damaged  and  were  then 
sold  at  a  loss  of  33^%.    What  was  the  loss  ? 

14.  Some  fruit  costing  $150  was  damaged  and  was  then 
sold  at  a  loss  of  20%.    What  was  the  loss  ? 

15.  Some  goods  left  over  from  the  holiday  trade  were 
sold  at  a  loss  of  20%.    They  cost  $150.    What  was  the 
selling  price  ? 

16.  A  dealer  who  was  overstocked  with  shoes  sold  $400 
worth  at  a  loss  of  12^%.   How  much  did  he  lose,  and  what 
was  the  selling  price  ? 


COMMISSION  155 

79.  Commission 

Find  the  commissions  on  the  following  amounts  at  the 
given  rates  : 

1.  $5,  1%.  5.  $5,  3%.  9.  $500,  3%. 

2.  $7,1%.  6.  $7,4%.  10.  $700,  4%. 

3.  $9,  1%.  7.  $9,  5%.  11.  $900,  5%. 

4.  $8,  6%.  8.  $9,  7%.  12.  $800,  8%. 

13.  What  is  the  commission  on  $2000  at  2£%  ? 

14.  If  you  bought  $8  worth  of  berries  for  a  grocer,  and 
received  5%  commission,  how  much  did  you  make  ? 

15.  If  a  salesman  sells  $800  worth  of  goods  and  receives 
4%  commission,  how  much  does  he  make  ? 

16.  If  a  wholesale  dealer  gives  a  salesman  3%  commis- 
sion on  $2000  worth  of  goods,  what  is  the  commission  ? 

80.  Commission 

Find  the  amounts  after  adding  the  following  commissions  : 

1.  $5,  2%.  4.  $8,  9%.  7.  $500,  5%. 

2.  $8,  5%.  5.  $8,  1£%.  8.  $600,  8%. 

3.  $7,  3%.  6.  $8,  2±%.  9.  $800,  \\%. 

10.  A  dealer  paid  $500  for  some  goods,  and  2%  to  the 
agent  who  bought  them  for  him.    What  was  the  total  cost  ? 

11.  A  dealer  received  $500  for  some  goods,  but  had  to  pay 
his  salesman  2  %  for  selling  them.  What  was  his  net  income? 

12.  A  merchant  sold  $2000  worth  of  goods,  but  paid  a 
commission  of  1%  on  the  sale.    What  was  his  net  income  ? 

13.  A  real  estate  broker  charged  2^%  for  selling  some 
land  for  $3000.   How  much  was  his  commission  ? 

14.  A  traveling  salesman  received  3^%  commission  for 
selling    $10,000   worth    of    goods.     How   much    was    his 
commission  ? 


156  PERCENTAGE 

81.  Finding  Interest 

Find  the  interest  for  1  yr.  at  the  given  rates  : 

1.  $100,  4%.  6.  $600,  4%.  11.  $700, 

2.  $100,  3%.  7.  $200,  5%.  12.  $900, 

3.  $300,  3%.  8.  $600,  5%.  13.  $100, 

4.  $250,  3%.  9.  $800,  5%.  14.  $200, 

5.  $250,  4%.  10.  $400,  6%.  15.  $400,          . 

16.  What  is  the  interest  for  1  yr.  on  $200  at  6%  ?  at  5%  ? 
at4%?   at4|%? 

17.  What  is  the  interest  for  1  yr.  on  $400  at  3%  ?  on 
$300  at  4%  ? 

18.  What  is  the  interest  for  1  yr.  on  $2000  at  5%  ?  at 
6%  ?  at  4^%  ? 

19.  What  is  the  interest  on  $1000  at  6%  for  1  yr.  ?  for 
£  yr.  ?  for  ^  yr.  ?  for  3  mo.  ?  for  £  yr.  ?  for  4  mo.  ? 

82.  Finding  Interest 

/     /rvfO   ' 

jPY/ic?  £Ae  interest  for  J  yr.  a£  £Ae  given  rates  per  year  : 

M7\$200,  4%:  f    /1}$700,  4%.  'Y     /5/$600,  5%. 
2.  $300,4%.    (,    !    4y'$400,  5%.  /  <Q 


_ 

£Ae  interest  for  |  yr.  a£  tf/46  given  rates  per  year  : 

(??  $300,  4%.    */        9.  $800,  6%.          dD  $800,  3%. 
8.  $400,  5%.  10.  $4QO,  2%.           ©$600,  6%. 

H^^ 

Find  the  interest  for  |  yr.  ai  i/ie  given  rates  per  year  : 

13.  $300,  5%.  15.  $700,  6%.  17.  $500,  6%. 

<g£>$600,4:%.     £    (2>?$600,  2%.j       18.  $300,  6%. 

19.  What  is  the  interest  on  $2000  at  6%  for  1  yr.  ? 

20.  What  is  the  interest  on  $4000  at  5%  for  1  yr.  ?    for 
6  mo.  ?   for  3  mo.  ?   for  l£  ino.  ? 


. INTEREST  157 

83.   Finding  Interest 

Find  the  interest  on  the  following : 

1.  $100,  6%,  1  yr.  10.  $500,  6%,  6  mo. 

2.  $400,  6%,  1  yr.  11.  $300,  5%,  4  mo. 

3.  $200,  5%,  1  yr.  12.  $900,  6%,  4  mo. 

4.  $900,  5%,  1  yr.  13.  $200,  6%,  3  mo. 

5.  $400,  4%,  1  yr.  14.  $900,  4%,  3  mo. 

6.  $700,  4%,  1  yr.  15.  $400,  6%,  1  mo. 

7.  $300,  3%,  1  yr.  16.  $900,  4%,  1  mo. 

8.  $800,  3%,  1  yr.  17.  $200,  2J%,  6  mo. 


x-,9.  $200,  6%,  6  mo.        <2X       18.  $400, 

19.  What  is  the  interest  on  $100,  at  6 %,f or  lyr.?  for2yr.? 

20.  What  is  the  interest  on  $200,  at  6  % ,  f or  1  y r.  ?  for  2  y r.  ? 

21.  What  is  the  interest  on  $500,  at  4  %,f or  IJyr.?  forl^yr.? 
•  22.  What  is  the  interest  on  $2000,  at  6%,  for  1  yr.  3  mo.  ? 

84.   Finding  Interest 

Find  the  interest  for  1  yr.  at  the  given  rates : 

1.  $12,  6%..  4.  $80,  5%.  7.  $300,  6%. 

2.  $25,  6%.  5.  $60,  4%.  8.  $500,  5%. 

3.  $15,  5%.'  6.  $90,  4%.  9.  $800,  4%. 

^'wc?  £/ie  interest  on  the  following  for  2  yr. : 

10.  $40,  6%.  12.  $70,  5%.  14.  $200,  6%. 

11.  $50,  6%.  13.  $90,  5%.  15.  $800,  5%. 

J^t'/ic?  t he  interest  on  the  following  for  6  mo. : 
16.  $80,  6%.  17.  $80,  5%.  18.  $70,  4%. 

jfznrf  the  interest  on  the  following  for  1  yr.  6  mo.: 
19.  $50,  6%.  20.  $60,  5%.  21.  $75;  4%. 


158  INTEREST 

85.  Finding  Interest 

Find  the  amount  of  principal  and  interest  for  1  yr.  : 

1.  $90,  6%.  /3.  $80,  5%.  5.  $700,  6%. 

2.  $80,  6%.  X4.  $90,  4%.  /6.  $900,  5%. 

Find  tlie  amount  of  principal  and  interest  for  2  yr.: 
7.  $70,  6%.  8.  $50,  6%.  9.  $2000,  5%. 

Find  the  amount  of  principal  and  interest  for  1  yr.  6  mo.: 

10.  $40,  6%.  11.  $300,  6%.  12.  $4000,  5%. 

Find  the  amount  of  principal  and  interest  for  2  yr.  Jf  mo. : 
13.  $50,  6%.  14.  $100,  6%.  15.  $6000,  5%. 

86.  Finding  Interest 

Find  the  interest  on  the  following : 

1.  $200,  6%,  2  yr.  6.  $300,  6%,  li  yr. 

2.  $200,  6%,  3  yr.  7.  $500,  3%,  1^  yr. 

3.  $300,  5%,  4  yr.  8.  $400,  4%,  1J  yr. 

4.  $500,  4%,  7  yr.  9.  $800,  5%,  2  yr.  6  mo. 

5.  $400,  5%,  1^  yr.  10.  $800,  5%,  2  yr.  3  mo. 

11.  How  does  the  income  on  $1500  at  6%  compare  with 
that  on  $3000  at  3%  ? 

12.  How  does  the  income  on  $2000  at  5%  compare  with 
that  on  $1500  at  6%  ? 

13.  How  does  the  income  on  $1200  at  4%  compare  with 
that  on  $1000  at  5%  ? 

Find  the  amount  of  principal  and  interest  for  2  yr.  3  mo. : 

14.  $50,  6%.  15.  $100,  4%.  16.  $4000,  5%. 


87.  Six  Per  Cent  Method 

As  the  rate  for  1  yr.  is  6  %,  for  60  da.  it  is  1%.  Therefore  the  interest 
on  $448  for  60  da.  at  6%  is  $4.48  ;  for  30  da.,  half  that,  or  $2.24  ;  for 
90  da.,  the  sum  of  these,  or  $6.72;  for  15  da.,  half  of  $2.24;  and  so 
for  other  periods. 

Find  the  interest  at  6°fc  for  60  da.  on  the  following : 

1.  $725.      3.  $500.      5.  $385.      7.  $750.      9.  $2500. 

2.  $675.      4.  $950.      6.  $530.      8.  $235.    10.  $3750. 

Find  the  interest  at  6°/0  for  30  da.  on  the  following : 

11.  $800.    12.  $640.    13.  $480.    14.  $360.    15.  $1600. 

Find  the  interest  at  6°f0  for  90  da.  on  the  following : 

16.  $600.  17.  $440.  18.  $820.  19.  $300.  20.  $2000. 

88.  Six  Per  Cent  Method 

Find  the  amount  of  principal  and  interest,  at  6°/0,  for  60 
da.,  on  the  following  : 

1.  $950.      2.  $730.      3.  $650.      4.  $870.      5.  $2500. 

Find  the  amount  at  6C/0  for  30  da.  on  the  following : 
6.  $200.      7.  $300.      8.  $500.      9.  $840.    10.  $2000. 

Find  the  amount  at  6°/c  for  90  da.  on  the  following : 

11.  $800.    12.  $240.    13.  $400.    14.  $600.    15.  $4000. 

Find  the  amount  at  6°10  for  10  da.  on  the  following  : 

16.  $600.    17.  $540.    18.  $360.    19.  $420.    20.  $2400. 

Find  the  interest  at  6°f0  for  63  da.  on  the  following : 

21.  $400.    22.  $800.    23.  $200.    24.  $600.    25.  $2000. 


V 


160  INTEREST 

89.  Interest 


1.  A  note  is  dated  March  10  and  is  due  on  May  9.    How 
many  days  has  it  to  run  ? 

\j  2.  The  note  in  Ex.  1  is  for  $1250  at  6%  interest.    What 
is  the  amount  of  principal  and  interest  on  May  9  ? 
/-i<,       3.  A  note  is  dated  March  10  and  is  due  on  June  8.    How 
many  days  has  it  to  run  ? 

\4.  The  note  in  Ex.  3  is  for  $1250  at  6%  interest.  What 
is  the  amount  of  principal  and  interest  on  June  8  ? 
i/  5.  A  jeweler  can  buy  $1225  worth  of  plated  ware  on  60 
days'  credit,  or  he  can  get  the  goods  for  $1200  in  cash, 
which  he  can  borrow  for  the  60  days  at  6%.  By  which  plan 
will  he  gain  the  more,  and  how  much  will  he  gain  ? 
___-».  6.  A  farmer  owes  $1500  on  his  farm.  He  keeps  the 
interest  paid  up,  and  pays  $650  on  the  principal  one  year 
and  $700  the  next  year.  He  finds  that  he  then  needs  only 
60  days  to  pay  the  balance.  How  much  will  this  balance 
be,  with  interest  for  the  60  da.  at  6%  ? 

7.  On  November  2  a  manufacturing  company  finds  that 
it  needs  $2500  until  January  1.    On  December  2  it  finds 
that  it  must  have  $1000  more.    It  borrows  this  money  at 
6%  and  pays  it  when  due.   What  is  the  amount  of  interest 
on  both  loans  ? 

8.  A  bank  loans  the  following  amounts  for  60  da.  at  6%  : 
^500,  $250,  $750,  $400,  $600.   How  much  interest  does  it 

receive  on  all  these  loans  together  ?    How  much  does  it 
receive  on  each  ? 

9.  A  bank  loans  to  a  merchant  $650  for  60  da.  and  $400 
for  30  da.,  both  at  6%.    How  much  interest  must  the  mer- 
chant pay  on  both  notes  ? 

«/. o  10.  A  merchant  borrows  $1500  from  a  bank  for  60  da.  at 
6%.  He  pays  the  interest  in  advance.  How  much  is  then 
left  from  the  $1500  ? 


RATE  AND  TIME  161 

90.  Finding  the  Rate 

If  the  interest  on  $300  for  6  mo.  is  §7.50,  for  1  yr.  it  is  $15.    $15  is 
^  Of  §300  or  Tjfo  of  it.    Hence  the  rate  is  5%. 

Given  the  principal,  interest,  and  time,  find  the  rate : 

1.  $300,  $5,  4  mo.  8.  $600,  $6,  2  mo. 

2.  $300,  $4.50,  3  mo.  9.  $700,  $84,  2  yr. 

3.  $400,  $10,  6  mo.  10.  $700,  $56,  2  yr. 

4.  $400,  $2,  1  mo.  11.  $800,  $120,  3  yr. 

5.  $500,  $5,  3  mo.  12.  $1000,  $240,  4  yr. 

6.  $500,  $12.50,  6  mo.  13.  $1000,  $110,  2  yr. 

7.  $600,  $10,  4  mo.  14.  $2000,  $180,  2  yr. 

15.  $10  is  what  per  cent  of  $250  ? 

16.  At  what  rate  must  $3000  be  loaned  to  produce  an 
income  of  $150  a  year  ? 


91.   Finding  the  Time 

If  the  interest  on  $300  at  5%  is  $7.50  for  a  certain  time,  then  since 

7   £*C\ 

the  interest  for  1  yr.  is  $15,  the  time  must  be  — —  of  1  yr.,  or  4  yr. 

15 

Given  the  principal,  interest,  and  rate,  find  the  time : 

1.  $100,  $10,  5%.  6.  $600,  $3,  6%. 

2.  $200,  $6,  6%.  7.  $700,  $84,  6%. 

3.  $300,  $3,4%.  8.  $800,  $20,  5%. 

4.  $400,  $4,  3%.  9.  $900,  $180,  4%. 

5.  $500,  $5,  4%.  10.  $1000,  $10,  3%. 

11.  How  long  will  it  take  $200  to  gain  $48  at  6%  ? 

12.  How  long  will  it  take  $750  to  gain  $7.50  at  6%  ? 

13.  How  long  will  it  take  $400  to  amount  to  $500  with 
interest  at  5%  ? 

14.  How  long  will  it  take  $100  to  double  itself  at  5%  ? 
How  long  will  it  take  $200  to  double  itself  at  5%  ? 


162  INTEREST 

92.   Reyiew 

1.  How  long  must  a  man  have  $500  invested  at  6%  so 
that  the  amount  of  principal  and  interest  may  be  $650? 

2.  A  man  borrowed  $6000  in  the  East  at  5%  and  in- 
vested it  in  the  West  at  8%.    How  much  did  he  make  per 
year  by  the  transaction  ? 

3.  What  sum  must  be  invested  at  6%  so  that  at  the  end 
of  three  years  the  interest  may  be  $90  ? 

4.  At  what  rate  must  $1000  be  invested  so  that  at  the 
end  of  two  years  the  amount  of  principal  and  interest  may 
be  $1090  ? 

5.  A  man  having  $4000  invested  at  5%  reinvests  half  of 
it  at  6%  and  the  other  half  at  4%.    What,  if  any,  is  the 
difference  in  income  ? 

6.  A  man  having  $10,000  invested  at  5£<%  reinvests 
half  of  it  at  6%  and  leaves  the  rest  as  before.    What  is 
the  increase  in  income  ? 

7.  During  the  year  a  merchant  borrows  at  various  times 
$500,  $700,  $1300,  $1500,  each  time  for  60  da.  at  6%.   How 
much  interest  does  he  pay  ? 

8.  A  bank  loans  $400  at  6%  and  receives  $6  interest 
(bank  discount).    Eequired  the  time. 

9.  A  bank  loans  $600  for  60  da.  and  receives  $5  inter- 
est.   Required  the  rate. 

10.  A  bank  loans  some  money  for  60  da.  at  6<%  and 
receives    $5  interest.    How  much  is   the  amount   of   the 
loan? 

11.  A  man  borrows  $1000  for  1  year  at  6%.   When  it  be- 
comes due  he  finds  that  he  needs  60  da.  more  time  to  pay 
the  principal  and  interest.    The  lender  agrees  to  this  if  the 
borrower  will  pay  interest  for  the  60  da.  on  the  amount  of 
principal  and  interest  for  the  year.    How  much  must  the 
borrower  pay  at  the  end  of  60  da.  ? 


RATIO  163 

V.    RATIO  AND  PROPORTION 

93.   Finding  Ratios 
The  ratio  of  8  to  10  is  T8ff  or  f . 
Find  the  ratio  of  the  first  number  to  the  second: 

1.  2,  4.  5.  5,  15.  9.  7,  49.  13.  2  ft.,  4  ft. 

2.  4,  2.  6.  5,  25.  10.  8,  50.  14.  4  in.,  6  in. 

3.  2,  8.  7.  6,  36.  11.  9,  36.  15.  6  yd,  9  yd. 

4.  8,  2.  8.  9,  12.  12.  6,  21.  16.  $8,  $9. 

17.  What  is  the  ratio  of  4  to  6  ?  4ft.  to  6ft.  ?  4%to6%? 

18.  What  is  the  ratio  of  6  to  8  ?  6  mo.  to  8  mo.?  $6  to  $8? 

19.  If  a  blackboard  is  20  ft.  long  and  5  ft.  high,  what  is 
the  ratio  of  height  to  length  ?    of  length  to  height  ? 

20.  If  a  schoolroom  is  40  ft.  long  and  25  ft.  wide,  what 
is  the  ratio  of  width  to  length  ?    of  length  to  width  ? 

94.   Finding  a  Ratio  Term 

X 

If  the  ratio  -  equals  10,  the  x  must  stand  for  the  number  that, 

2 
divided  by  2,  equals  10.    Therefore  x  must  stand  for  20. 

Find  the  number  represented  by  x  : 


1. 

—  4 

4.  ± 

=  5. 

_   a, 

u 

10. 

X 

A 

2 

5 

'  8 

~4~' 

12 

3' 

2. 

x    '1 

5.  X- 

_1 

8.  - 

_1 

11. 

x 

3 

3~ 

6 

~  2' 

9 

~3' 

16  ~ 

4' 

3. 

x-3 

6    X 

1 

9    x 

_1 

12. 

*  _ 

4 

4 

''  7 

7' 

'  6 

3' 

15 

5' 

13.  What  number  has  to  18  the  ratio  f  ? 

14.  Th^ratio  of  the  height  of  a  schoolroom  to  its  width 
is  f .    The  width  is  20  ft.    What  is  the  height  ? 

15.  The  ratio  of  the  length  of  a  window  pane  to  its  width 
is  $.    The  width  is  12  in.    What  is  the  length  ? 


cc      2 

x_  6 

9 

1        —   t 

7         — 

"2      4 

6      18 

9      3' 

,    x      4 

*       6 

x       3 

o    

o           /? 
u         D 

7~2l' 

8-To  =  5 

«       2 

a;       1 

a;       1 

3       ~™  —    . 

£J        t 

9    -  =  -  . 

5      10 

8      2 

2      3 

164  RATIO  AND  PROPORTION 

95.   Finding  the  Missing  Term 

Think  of  the  proportion  x :  3  =  8  : 12  in  the  more  familiar  form  of 

2 

equal  fractions,  -  =  —    Multiply  both  by  3,  and  x  =  —  — ,  or  2. 
3      12  I J 

Find  the  value  of  x : 

io-H- 

v        9 
* 

4  =  5" 
x      5 

5  6 

13.  What  number  has  to  3  the  ratio  of  8  to  6  ? 

14.  The  last  three  terms  of  a  proportion  are  2,  4,  8.  What 
is  the  first  term  ? 

15.  What  number  has  to  30  the  ratio  of  5  to  6  ? 


96.   Finding  the  Missing  Term 

Think  of  the  proportion  5  :  x  =  15 : 18  as  -  =  —  ;  then  see  that 

6  *      18 

x      18  ?  x  #      . 

-  =  — ,  and  x  — =  6. 

6      16  jp 


Find  the  value  of  x : 

'  a;  ~~  4  '          "  ie  ~  3  '  '  x~2'        10'^T~"3 

2_4  ,5_10  .    8  _  4  11_22 

*T         t'x~20'  a~3"  'T=:T 

3  =  1  6    *>_3  Q    ?.  =  3  ia»12  =  6 

*        9  '  »        9'  »        7  'y          7  ' 

•V  41  t*s  +J  mf  t  dv  I 

13.  To  what  number  has  5  the  ratio  of  1  to  3  ? 

14.  To  what  number  has  15  the  ratio  of  3  to  4  ? 


PROPORTION  165 

97.    Similar  Figures 

1.  In  this  figure,  if  AB  represents  2  in.,  AD  3  in.,  and 
EC  1  in.,  what  does  DE  represent  ? 

2.  If  AB  represents  1  in.,  BC  |  in., 
and  DE  3  in.,  what  does  A  D  represent  ? 

3.  If  AC  represents  2  in.,  AE  3  in., 
and  AB  1  in.,  what  does  AD  represent  ? 

4.  If  when  the  diameter  of  a  circle  is  100  in.  the  cir- 
cumference is  314  in.  (as  it  is  nearly),  what  is  the  circum- 
ference when  the  diameter  is  10  in.  ?   50  in.  ? 

5.  If  when  the  side  of  an  equilateral  triangle  is  20  in. 
the  height  is  17.3  in.  (as  it  is  nearly),  what  is  the  height 
when  the  side  is  100  in.  ? 

6.  If  a  box  is  to  be  made  10  in.  long,  and  is  to  have  the 
same  proportions  as  another  box  that  is  4  in.  wide  and  5  in. 
longpiow  wide  must  the  new  box  be  ? 

98.   Review 

1.  If  a  pound  of  grass  contains  11  oz.  of  water,  how  much 
water  will  7  Ib.  contain  ? 

2.  If  2  packages  of  paper  cost  60/,  what  will  7  packages 
cost? 

3.  If  2  cu.  ft.  of  water  weigh  125  Ib.,  what  is  the  weight 
of  20  cu.  ft.  ?    of  10  cu.  ft.  ? 

4.  If  3  bu.  of  beans  weigh  180  Ib.,  what  is  the  weight  of 
Ibu.?    of2bu.  ? 

5.  If  5  bu.  of  dried  apples  weigh  130  Ib.,  what  is  the 
weight  of  10  bu.  ?    of  1  bu.  ? 

6.  If  10  bu.  of  oats  weigh  320  Ib.,  what  is  the  weight  of 
1  bu.  ?    of  5  bu.  ? 

7.  If  1  cu.  ft.  of  sulphur  weighs   125  Ib.,  what  is  the 
weight  of  4  cu.  ft.  ?    of  5  cu.  ft.  ? 


166  REVIEW 

99.  Review 

1.  What  is  the  perimeter  of  a  square  5  ft.  9  in.  on  a  side  ? 

2.  At  28/  a  dozen,  what  will  l£  doz.  eggs  cost  ? 

3.  At  16/  a  pound,  what  will  If  Ib.  of  meat  cost  ? 

4.  If  you  buy  1J  doz.  eggs  at  30/  a  dozen,  what  change 
should  you  receive  from  50/"  ? 

5.  If  you  buy  2^  Ib.  of  figs  at  18/  a  pound,  what  change 
should  you  receive  from  $1  ? 

6.  If  you  buy  12^  yd.  of  velvet  at  $2  a  yard,  what  change 
should  you  receive  from  $30  ?  ^^B? 

7.  If  you  buy  15  Ib.  of  sugar  at  6/  a  pound,  anql  ^f)/  can 
of  tomatoes,  should  you  receive  any  change  from  $li 

8.  What  is  the  ratio  of  the  perimeter  of  a  triangmlf  ft. 
on  each  side  to  that  of  a  square  2J  ft.  on  a  side? mo  that 
of  a  square  5  ft.  on  a  side  ? 

100.  Review 

1.  Find  the  perimeter  of  a  square  1  ft.  9  in.  on  a  side. 

2.  Find  the  perimeter  of  a  parallelogram  two  of  whose 
sides  are  3  ft.  4  in.  and  2  ft.  2  in. 

3.  If  the  perimeter  of  a  square  is  9  ft.  4  in.,  how  long 
is  its  side  ? 

4.  If  the  perimeter  of  an  equilateral  (equal-sided)  tri- 
angle is  6  ft.  9  in.,  how  long  is  each  side  ? 

5.  Into  how  many  parts,  each.f  in.  long,  can  I  divide  a 
line  that  is  3f  in.  long  ? 

6.  If  a  box  is  8  in.  long,  2  in.  high,  and  4  in.  wide,  what 
is  the  sum  of  all  its  12  edges  ? 

7.  If  the  circumference  of  a  circle  is  3 j  times  its  diame- 
ter, what  is  the  diameter  when  the  circumference  is  12f  in.? 

8.  If  two  sides  of  a  triangle  are  .3  ft.  7  in.  and  3  ft.  9  in., 
and  the  perimeter  is  10  ft.  8  in.,  what  is  the  third  side  ? 


CHAPTEE  IV 

I.    FUNDAMENTAL  OPERATIONS.    BUSINESS 
PROBLEMS 

1.  Addition 

1.  70  +  50.  7.  4.8  +  2.2.  13.  125  +  60.    I 

2.75  +  50.  8.  4.S  +  2.7/  14.125  +  65.     ^c 

3.  75  +  55.  9.  .73  +  .27.  15.  125  +  67.    >  ^ 

4.  75  +  57.  10.  .73  +  .29.  H>'  16.  1.45  +  .37.  • 

5.  2.7  +  3.3.    <  f  11.  .85  +  .67.i  :-•  17.  2.25  +  .75. 

6.  2.7  +  3.8.'*-    12.  .94 +.78.  •- <  18.  3.45  +  .55. 
19.  Find  the  sum  of  165  and  39 ;  of  16.5  ft.  and  3.9  ft. 

2.  Addition 

1.  12ft.  7  in. +  6  ft.  9  in.         5.  27  gal.  2  qt. +17  gal.  3  qt. 

2.  51b.  10oz.  +  31b.  8oz.         6.  7  mi.  126  ft. +  3  mi.  75ft. 

3.  15yd.  8  in. +9  yd.  30  in.      7.  17  rd.  12ft.  +  15rd.  4i  ft. 

4.  8bu.  2pk.+15bu.  3pk.     8.  25  wk.  6da.  +  17wk.  5  da. 
9.  Find  the  sum  of  8  Ib.  9  oz.  and  9  Ib.  8  oz. 

10.  The  three  sides  of  a  triangle  are  7  ft.  3  in.,  6  ft.  4  in., 
and  6  ft.  8  in.    What  is  the  perimeter  ? 

11.  The  four  sides  of  a  field  are  25  rd.  6  ft.,  32  rd.,  25  rd. 
10£  ft.,  and  32  rd.    What  is  the  perimeter  ? 

12.  A  lady  buys  27|  yd.  of  cloth  and  finds  that  she  needs 
30  in.  more.    How  much  cloth  did  she  need  in  all  ? 

13.  If  I  pay  $2.75  for  groceries  and  85/  for  meat,  how 
much  do  I  pay  for  both  ?  • 

167 


168  FUNDAMENTAL  OPERATIONS 

3.   Bank  Accounts 

Find  the  sums  of  the  following  deposit-slip  items : 
1.  Bills  $50,  silver  $35,  checks  $70. 


2.  Bills  $75,  silver  $40,  checks 

3.  Bills  $80,  silver  $30,  checks  $75. 

4.  Bills  $60,  silver  $20,  checks  $85. 

5.  Bills  $125,  silver  $25,  checks  $92. 

6.  Bills  $160,  silver  $35,  checks  $87. 

7.  Bills  $270,  silver  $40,  checks  $190. 

8.  Bills  $250,  silver  $20,  checks  $245. 

9.  Bills  $275,  silver  $40,  checks  $250. 

10.  Bills  $300,  silver  $50,  checks  $475. 

11.  Bills  $250,  gold  $100,  silver  $40,  checks  $310. 

12.  Bills  $500,  gold  $250,  silver  $30,  checks  $120. 

4.   Bank  Accounts 

Find  the  sums  of  the  following  deposit-slip  items  : 

1.  Bills  $375,  gold  $125,  silver  $75,  checks  $475. 

2.  Bills  $450,  gold  $100,  silver  $50,  checks  $375.50. 

3.  Bills  $575,  gold  $125,  silver  $50,  checks  $455.75. 

4.  Checks  for  $52.40,  $2.60,  $5,  $40,  $100. 

5.  Checks  for  $25,  $35,  $40,  $22.30,  $2.70;   $75  in 
bills. 

6.  Checks  for  $22,  $37,  $60,  $40.50,  $28.50 ;  $50  in 
bills. 

7.  Checks  for  $42,  $51,  $67,  $50,  $100r  $35.25 ;  $25 
in  bills. 

8.  Checks  for  $125,  $250,  $300,  $50,  $75,  $125.50; 
$100  in  bills. 

9.  Checks  for  $25,  $50,  $120,  $240,  $65,  $500,  $1000 ; 
$100  in  bills. 


ADDITION  169 

5.  Addition  of  Common  Fractions 

1.  *  +  f .  6.  i  +  |.  11.  i  +  TV  16.  |  +  TV 

2.  i  +  |.  7.  I  +  f.  12.  |  +  TV  17.  £  +  gy 

3.  i  +  |.  8.  f  +  |.  13.  i  +  TV  18.  i  +  ^V 

4.  *  +  f .  9.  TV  +  i-  14.  |  +  TV  19.  i  +  &. 

5.  i  +  i.  10.  i  +  ft.  15.  i  +  A-  20.  I  +  M- 

21.  If  a  veneer  of  ft  in.  is  put  on  a  |-in.  board,  how 
thick  is  the  board  with  the  veneer  ? 

22.  If  a  publisher  decides  to  change  a  book  margin  of 
f  in.  by  increasing  it  ft  in.,  what  will  the  margin  then  be  ? 

23.  If  a  cylindrical  iron  rod  f  in.  thick  is  covered  with 
brass  ft  in.  thick,  what  is  then  the  thickness  of  the  rod  ? 

24.  If  the  thickness  of  a  book,  without  the  cover,  is  |  in., 
and  if  each  of  the  cover  boards  is  ^  in.  thick,  how  thick  is 
the  bound  book  ? 

6.  Addition  of  Mixed  Numbers 

IOltOl  ^        K  ^l       i      0 1  1  1        O  /I  ^       i      ^?  1 

.   Z%  +  o^.  6.    Of  +  Z§.  11.    Z4j  +  b^. 

2.  3J  +  5|.  7.  6|  +  5J.  12.  33^  -f  12£. 

3.  7i  +  6f  8.  7§  +  51.  13.  66.1  +  12^. 

4.  3f  +  2i.  9.  8£  +  1\.  14.  16§  +  66§. 

5.  4|  +  6£.  10.  22^  +  5%.  15.  87i  +  33^. 

16.  If  a  skirt  28^  in.  long  has  a  ruffle  3|  in.  wide  sewed 
on,  how  long  is  the  skirt  ? 

17.  If  a  curtain  23T\  in.  wide  has  a  lace  edge  2|  in.  wide 
sewed  down  one  side,  what  is  then  the  width  ? 

18.  If  a  carpet  rug  3|  yd.  wide  without  the  border  has 
a  border  |  yd.  wide  sewed  around  it,   how  wide  is  the 
rug  then  ? 

19.  If  a  picture  is  framed  so  as  to  show  15|  in.  in  width, 
and  if  the  frame  is  2\  in.  wide,  what  is  the  total  width  of 
picture  and  frame  ? 


170                  FUNDAMENTAL  OPERATIONS 

7.   Review.  Interest 

Find  the  interest  on  the  following  for  the  time  and  the 
rate  specified  : 

1.  $200,  5  yr.,  6%.  6.  $800,  3  mo.,  6%. 

2.  $300,  6  mo.,  6%.  7.  $400,  2  yr.,  5%. 

3.  $400,  2J-  yr.,  6%.  8.  $1200,  2'  yr.,  5%. 

4.  $250,  4  yr.,  6%.  9.  $2000,  1  yr., 

5.  $500,  4  yr.,  6%.  10.  $4000,  1  yr., 


Find  the  amount  of  principal  and  interest  : 

11.  $100,  2  yr.,  6%.  16.  $600,  8'  mo.,  6%. 

12.  $200,  3  mo.,  6%.  17.  $700,  6  mo.,  6%. 

13.  $300,  3  yr.,  6%.  18.  $800,  10  mo.,  6%. 

14.  $400,  1  mo.,  6%.  19.  $900,  2  yr.,  5%. 

15.  $500,  2  mo.,  6%.  20.  $1000,  3  yr.,  5%. 

8.   Review.   Interest 

Compute  the  interest  in  the  following  cases  : 

1.  $400,  5  yr.,  6%.  4.  $500,  6  yr.,  4%. 

2.  $400,  6  yr.,  5%.  5.  $600,  4  yr.,  5%. 

3.  $500,  4  yr.,  6%.  6.  $600,  5  yr.,  4$. 

7.  What  is  the  compound  interest  on  $100  for  2  yr.  at 
3%,  the  interest  being  compounded  annually  ? 

8.  A  man  gives  his  note  for  $300  for  1  yr.  at  6$.    At 
the  end  of  the  year  he  pays  the  interest  and  $100  of  the 
principal,  and  the  time  is  extended  on  the  balance  a  j^ear. 
How  much  is  due  at  the  end  of  the  second  year  ? 

9.  A  man  gives  his  note  for  $500  for  two  years  at  Q°fc. 
At  the  end  of  the  two  years  he  pays  $260  and  the  time  is 
extended  on  the  balance.    How  much  is  due  at  the  end  of 
the  next  year  ? 


SUBTRACTION  171 

9.   Subtraction 

1.  60-37.  6.  64-39.  11.  93-64.  16.  23.3-7.5. 

2.  52-28.  7.  52-27.  12.  121-67.  17.  6.5-2.7. 

3.  41-26.  8.  48-29.  13.  .98 -.49.  18.  8.7-2.9. 

4.  62-36.  9.  81-56.  14.  .45 -.26.  19.  4.1-2.5. 

5.  71-27.  10.  84-45.  15.  9.6-2.8.  20.  .125 -.06. 

21.  How  much  must  be  added  to  $250  to  make  $1100? 

22.  How  much  more  is  21.7  mi.  than  9.2  mi.? 

23.  If  I  buy  goods  for  $1.25  and  80/,  how  much  change 
should  I  receive  from  $5  ? 

24.  If  a  farmer  sells  produce  to  a  grocer  for  $5.50  and 
$6.25,  and  buys  groceries  costing  $1.75,  how  much  balance 
is  due  him  ? 

25.  If  a  man  buys  goods  to  the  amount  of  $640,  and 
pays  $180  down,  how  much  is  still  due?    If  he  pays  $460 
more,  how  much  is  then  due  ? 

10.   Subtraction 

1.  12  ft.  4  in.  -  3  ft.  8  in. 

2.  32  ft.  6  in.  -  12  ft.  9  in. 

3.  62  rd.  12  ft.  -  28  rd.  6  ft. 

4.  3  yr.  6  mo.  —  1  yr.  8  mo. 

5.  32  gal.  2qt.  -15  gal.  3  qt. 

6.  4  yr.  6  mo.  15  da.  —  8  mo.  1 0  da. 

7.  42  bu.  1  pk.  -  12  bu.  2  pk. 

8.  125  Ib.  6  oz.  -  24  Ib.  10  oz. 

9.  A  box  2  ft.  2  in.  long  and  1  ft.  10  in.  wide  is  how 
much  longer  than  wide  ? 

10.  A  note  made  September  20,  due  in  one  year,  has  a  pay- 
ment the  following  July  12.    How  long  has  it  then  to  run? 

11.  How  long  is  it  from  5  min.  past  6  P.M.  to  15  min.  past 
4  A.M.  of  the  next  day  ? 


172  FUNDAMENTAL  OPERATIONS 

* 

11.  Bank  Balances 

1.  A  man's  balance  in  the  bank  yesterday  was  $635. 
To-day  he  gives  a  check  for  $75.    What  will  be  his  balance 
after  the  check  is  cashed  ? 

2.  A   man's  balance  in  the  bank  yesterday  was  $800. 
To-day  his  Checks  for  $25  and  $160  are  cashed.   What  will 
be  his  balance  to-night  ? 

The  first  of  these  amounts  is  a  man's  balance  in  the  bank 
yesterday,  and  the  second  is  the  amount  checked  out  to-day. 
Find  the  balance  to-night : 

3.  $250,  $75.  7.  $350,  $35.  11.  $730,  $45. 

4.  $420,  $30.  8.  $560,  $70.  12.  $810,  $60. 

5.  $250,  $45.  9.  $575,  $90.  13. 

6.  $280,  $75.  10.  $620,  $80.  14. 

12.  Bank  Balances 

1.  A  man's   balance   in  the   bank  yesterday  was  $750. 
To-day  he  deposits  $150,  and  his  checks  for  $50  and  $125 
are  cashed.    What  will  be  his  balance  to-night  ? 

Given  the  following  balances  yesterday  and  the  checks  of 
to-day,  find  the  balances  to-night : 

2.  Balance,  $500 ;  checks,  $50,  $25,  $75. 

3.  Balance,  $600  ;  checks,  $100,  $50,  $25. 

4.  Balance,  $800 ;  checks,  $250,  $10,  $40. 

5.  Balance,  $1250;  checks,  $150,  $75,  $25. 

6.  Balance,  $1525;  checks,  $50,  $12.50,  $37.50. 

7.  Balance,  $1100  ;  checks,  $100,  $75,  $25,  $200. 

8.  Balance,  $750;  checks,  $10,  $30,  $50,  $100,  $10. 

9.  Balance,  $1475  ;  checks,  $75,  $30,  $20,  $75,  $275, 
$500,  $100. 


SUBTRACTION  173 

13.    Subtraction  of  Common  Fractions 

1-    *  -  *•  6-    i  -  TV  11.    I  -  TV  16.    I  -  &. 

2.  i  -  f  7.  i  -  TV  12.  |  -  TV  17.  ^  -  ?V 

3.  |  -  f  8.  |  -  TV  13.  |  -  TV  18.  &  -  ?V 

4.  |  -  f .  9.  |  -  TV  U.  f  -  TV  19.  A  -  4'V 

5.  i  -  TV  10.  i  -  TV  15.  |  -  ^.  20.  if  -  A- 

21.  How  much  thicker  is  a  |-inch  board  than  a  £-inch 
board  ? 

22.  How  much  longer  is  a  f  l-inch^line  than  a  J-inch  line  ? 

23.  How  much  thicker  is  a  i-inch  veneer  than  one  that  is 
TV  in.  thick  ? 

24.  If  the  perimeter  of  a  triangle  is  f  mi.,  and  two  sides 
are  .3  mi.  and  .2  mi.,  what  is  the  length  of  the  third  side  ? 

25.  If  a  field  is  f  mi.  long  and  T3ff  mi.  wide,  the  length 
is  how  much  greater  than  the  width  ? 

14.    Subtraction  of  Mixed  Numbers 

1.  3o£  -  17f  6.  51|  -  30i.  U.  782  _  33 j. 

2.  66§  -  33£.  7.  55f  -  35$.  12.  125^  -  SOJ. 

3.  25£  -  12J.  8.  63|  -  22J.  13.  116§  -  33^. 

4.  42|  -  20£.  9.  68  J  -  35  J.  14.  122^  -  32TV 

5.  471  -  22f  10.  75^  -  25^.  15.  157.5  -  27i. 

16.  What  must  be  subtracted  from  0.75  to  make  i  ? 

o 

17.  What  must  be  added  to  0.12^  to  make  f  ?    to  make  1  ? 

18.  If  a  book  page  is  7.25  in.  long  and  4|  in.  wide,  its 
length  is  how  much  greater  than  its  width  ? 

19.  If  a  book  page  is  4|  in.  wide,  and  if  the  inner  margin 
is  \  in.  and  the  outer  one  f  in.,  what  is  the  width  of  the 
printed  part  ? 

20.  If  a  flower  bed  27|  ft.  long  and  12^  ft.  wide  has  a 
walk  3  ft.  wide  around  it  on  the  outside,  how  long  and  how 
wide  is  the  bed  with  the  walk  ? 


174  FUNDAMENTAL  OPERATIONS 

15.  Review 

1.  From  1  take  the  sum  of  \  and  ^. 

2.  If  |  of  a  man's  property  is  invested  in  business,  T3ff 
in  bonds,  and  the  rest  in  banks,  what  part  is  in  banks  ? 

3.  If  a  man  divides  his  bank  deposits  among  three  banks 
so  that  the  first  receives  ^  of  the  deposits  and  the  second  J, 
what  part  does  the  third  receive  ? 

4.  A  merchant  reinvests  |  of  his  year's  income  in  his 
business,  spends  T7B   of  it,   and  saves  the  balance.    What 
part  of  his  income  does  he  save  ? 

5.  The  net  income  from  a  certain  business  amounted  to 
$3200  the  first  half  of  last  year  and  $2400  the  second  half. 
It  was  agreed  between  the  two  partners  that  the  first  should 
have  |  of  the  income  and  the  second  the  balance.    What 
was  the  income  of  the  second  for  the  whole  year  ? 

16.  Review 

1.  A  firm  has  $4800  in  the  bank  at  the  close  of  a  week's 
business.    During  the  following  week  it  deposited  $700  and 
checked  out  $1100.    What  was  its  balance  at  the  close  of 
that  week  ? 

2.  A  firm   takes  in  during  a   day  $720.    It  pays  out 
during  the  day  $35  for  help,  $200  for  new  goods,  $100 
for  the  week's  rent,  and  deposits  the  rest    in  the  bank. 
How  much  does  it  deposit  ? 

3.  A  dealer  in  cattle  buys  six  cows,  paying  for  them  $55, 
$60,  $65,  $45,  $50,  and  $70  respectively.    How  much  does 
he  pay  for  all  ? 

4.  A  man  earned  $3.75  on  Monday,  $2.50  on  Tuesday, 
$4.50  on  Wednesday,  and  $3.25  on  Thursday.    How  much 
did  he  earn  on  all  four  days  ?    How  much  more  must  he 
earn  to  make  the  total  $20  ? 


MULTIPLICATION  175 

17.  Multiplication 

Think  of  11  x  32  as  320  +  32,  or  352  ;  and  of  11  x  6.1  as  61  +  6.1, 
or  67.1. 

1.  2  x  75.  6.  4  x  73.  11.  7  x  82.  16.  9  x  .92. 

2.  2  x  86.  7.  5  x  92.  12.  7  x  8.2.  17.  11  x  63. 

3.  3  x  64.  8.  5  x  88.  13.  8  x  72.  18.  11  x  72. 

4.  3  x  77.  9.  6  x  42.  14.  8  x  .72.  19.  20  x  35. 

5.  4  x  56.  10.  6  x  4.2.  15.  9  x  92.  20.  30  x  72. 

21.  At  ll/  each,  what  will  2  doz.  slates  cost  ? 

22.  At  35/  each,  what  will  11  arithmetics  cost  ? 

23.  At  20/  a  dozen,  what  will  15  doz.  pencils  cost  ? 

24.  At  30/  a  dozen,  what  will  a  gross  of  pencils  cost  ? 

25.  At  24  /  a  yard,  what  will  6  yd.  of  cloth  cost  ?  6£  yd.? 

26.  At  50  /  a  yard,  what  will  65  yd.  of  matting  cost  ? 

27.  At  60/  a  yard,  what  will  45  yd.  of  carpet  cost? 

18.  Multiplication 

Think  of  11  x  12  ft.  2  in.  as  120  ft.  +  12  ft.  and  20  in.  +  2  in.,  or 
132  ft.  22  in.,  or  133ft.  10  in. 

1.  6  x  3  ft.  8  in.  7.  6  x  12  gal.  1  pt. 

2.  4  x  8  ft.  6  in.  8.  8  x  15  gal.  2  qt. 

3.  3  x  6  rd.  5J.  ft.  9.  8  x  22  Ib.  2  oz. 

4.  5^  x  4  rd.  1  yd.  10.  11  x  14  Ib.  1  oz. 

5.  7  x  8  yd.  6  in.  11.  12  x  30  Ib.  3  oz. 

6.  8  x  9  yd.  4£  in.  12.  25  x  44  Ib.  1  oz. 

13.  What  is  the  perimeter  of  a  square  that  is  6  rd.  4^  ft. 
on  a  side  ? 

14.  The  sides  of  a  triangular  lot  are  each  12  rd.  5^  ft. 
What  is  the  perimeter  ? 

15.  A  certain  pump  raises  100  cu.  ft.  of  water  a  minute. 
W7ater  weighing  62 \  Ib.  per  cubic  foot,  what  is  the  weight 
of  the  water  raised  per  minute  ? 


176  FUNDAMENTAL  OPERATIONS 

19.  Review.    Bank  Discount 

Find  the  discount  on  the  following  notes  : 

1.  $85,  2  mo.,  6%.  7.  $800,  3  mo.,  6%. 

2.  $90,  2  mo.,  6%.  8.  $1400,  3  mo.,  6%. 

3.  $350,  2  mo.,  6%.  9.  $1800,  2  mo.,  4%. 

4.  $775,  2  mo.,  6%.  10.  $2400,  2  mo.,  5%. 

5.  $400,  1  mo.,  6%.  11.  41200,  3 mo.,  6%;  also  5%. 

6.  $500,  1  mo.,  6%.  12.  $2400, 3 mo.,  6%;  also5%. 

13.  A  man  gave  a  note  for  $500  to  run  from  January  10 
to  February  9.    What  was  the  discount  at  6%  ? 

14.  How  much  is  the  discount  on  a  note  of  $1000,  at 
6%,  from  July  6  to  September  4  ?  from  July  6  to  August  5  ? 

15.  How  much  is  the  discount  on  a  note  of  $3000,  at  6%, 
from  October  3  to  November  2  ?    to  December  2  ? 

20.  Review.    Bank  Discount 

Find  the  proceeds  on  the  following  notes  : 

1.  $70,  2  mo.,  6%.  7.  $120,  1  mo.,  6%. 

2.  $75,  2  mo.,  6%.  8.  $120,  1  mo.,  5%. 

3.  $80,  2  mo.,  6%.  9.  $400,  1  mo.,  6%. 

4.  $85,  2  mo.,  6%.  10.  $1200,  1  mo.,  5%. 

5.  $60,  1  mo.,  6%.  11.  $3000,  2  mo.,  5%. 

6.  $60,  1  mo.,  5%.  12.  $3600,  2  mo.,  4%. 

13.  How  much  are  the  proceeds  on  a  note  of  $500,  due 
in  60  days  without  interest,  discounted  at  6%  ? 

14.  If  I  have  a  note  for  $80  due  in  90  days  without 
interest,  and  I  discount  it  at  Q°/0  to-day,  what  are  the 
proceeds  ? 

15.  A  note  of  $1200,  due  in  30  days  without  interest,  is 
discounted  at  6%.    What  are  the  proceeds?   What  would 
be  the  proceeds  if  the  note  were  discounted  at  5%? 


MULTIPLICATION  177 

21.   Multiplication  of  Common  Fractions 

1.  8  x  f .  7.  32  x  TV  13.  tV  of  32.  19.  f  of  f . 

2.  4  x  |.  8.  64  x  TV  14.  T&  of  64.  20.  |  of  f . 

3.  2  x  |.  9.  §  of  36.  15.  T\  of  60.  21.  f  of  f. 

4.  5  x  § .  10.  |  of  3.6.  16.  TV  of  7.2.  22.  T\  of  f . 

5.  15  x  f.  11.  f  of  35.  17.  f  of  f .  23.  ^  of  f. 

6.  16  x  |.  12.  |  of  4.8.  18.  |  of  f  24.  TV  of  T\. 

25.  How  much  is  £  of  half  an  inch  ? 

0 

26.  How  much  is  f  of  0.15  mi.  ? 

27.  Express  \  of  0.5  mi.  as  a  common  fraction. 

28.  Express  f  of  0.75  mi.  as  a  common  fraction. 

29.  Express  £  of  0.4  mi.  as  a  decimal  fraction ;  as  a  com- 
mon fraction. 

30.  Express  f  of  0.16  mi.  as  a  decimal  fraction;    as  a 
common  fraction. 

22.   Multiplication  of  Mixed  Numbers 

1.  5  x  15f .  7.  9  x  HJ.  13.  12  x  12£. 

2.  4  x  20£.  8.  4  x  12^.  14.  20  x  12£. 

3.  6  x  12£.  9.  2  x  45|.  15.  30  x  20$. 

4.  6  x  16f.  10.  10  x  37f  16.  16|  x  60. 

5.  3  x  33^.  11.  10  x  87£.  17.  33^  x  90. 

6.  12  x  llf .  12.  11  x  22TV  18.  66f  x  30. 

19.  How  much  is  l£  x  0.5  ? 

20.  How  much  is  2i  x  0.4  ? 

21.  How  much  is  \  of  f  of  0.8  ? 

22.  Express  2i  x  f  as  a  common  fraction ;  as  a  decimal 
fraction. 

23.  What  is  the  perimeter  of  a  triangle  16|  in.  on  each 
side? 

24.  What  is  the  perimeter  of  a  square  each  side  of  which 
is  17     in.? 


178  FUNDAMENTAL  OPERATIONS 

23.  Partial  Payments 

1.  A  note  for  $100,  at  6^,,  has  a  payment  of  $6  indorsed 
annually  for  2  years,  and  a  payment  of  $56  at  the  end  of 
the  third  year.    How  much  is  then  due  ? 

2.  A  note  for  $200,  at  6%,  has  a  payment  of  $12  indorsed 
at  the  end  of  the  first  year  and  $112  at  the  end  of  the 
second  year.    How  much  is  then  due  ? 

3.  A  note  for   $500,  at   6%,  has   a  payment  of  $430 
indorsed  at  the  end  of  the  first  year.    No  payments  are 
made  the  second  or  third  years.    How  much  is  due  at  the 
end  of  the  fourth  year  ? 

4.  A  note  for   $1000,   at  5%,  has  a  payment  of   $50 
indorsed  at  the  end  of  the  first  year,  $50  at  the  end  of  the 
second  year,  and  nothing  during  the  third  year.    How  much 
is  due  at  the  end  of  the  third  year  ? 

24.  Partial  Payments 

1.  A  note  for  $2500,  at  4%,  has  $100  a  year  indorsed 
for  the  first,  second,  and  third  years.    At  the  end  of  the 
fourth  year  $600  is  indorsed.    How  much  is  due  at  the  end 
of  the  fifth  year  ? 

2.  A  note  for  $3000,  at  4%,  has  $1120  indorsed  at  the 
end  of  the  first  year,  and  $1080  at  the  end  of  the  second 
year.    How  much  is  due  at  the  end  of  the  third  year  ? 

3.  A  note  for  $2000,  at  5%,  has  $1100  indorsed  at  the 
end  of  the  first  year,  and  $550  at  the  end  of  the  second 
year.    How  much  is  due  at  the  end  of  the  second  year  ?  at 
the  end  of  the  third  year  ? 

4.  A  note  for  $4000,  at  6%,  has  $240  indorsed  at  the 
end  of  the  first  year,  $240  at  the  end  of  the  second  year, 
and  $3240  at  the  end  of  the  third  year.    How  much  is  due 
at  the  end  of  the  fourth  year  ? 


DIVISION  179 

25.   Division 


1. 

78  + 

2. 

6. 

8.1 

+  3. 

11. 

65  + 

4. 

16. 

134 

+  5. 

2. 

9.6  + 

2. 

7. 

76- 

-3. 

12. 

123  +  4. 

17. 

9.6- 

-6. 

3. 

65  + 

2. 

8. 

101 

+  3. 

13. 

8.5  + 

5. 

18. 

.91  - 

*-  7. 

4. 

109  +  2. 

9. 

7.6 

+  4. 

14. 

91  + 

5. 

19. 

.96- 

-8. 

5. 

72  + 

3. 

10. 

9.2 

+  4. 

15. 

63  + 

5. 

20. 

.126 

+  9. 

21.  If  one  dictionary  costs  $6,  how  many  dictionaries  can 
be  bought  for  $96  ? 

22.  If  a  dozen  copies  of  a  certain  book  cost  $6.60,  how 
much  does  each  copy  cost  ? 

23.  If  a  perimeter  of  a  polygon,  each  of  whose  sides  is 
13  ft.,  is  78  ft.,  how  many  sides  are  there  ? 

24.  If  a  man  buys  4  Texas  saddle  horses,  paying  $90, 
$100,  $110,  and  $160  for  them,  what  is  the  total  cost? 
What  is  the  average  price? 

26.   Division 

1.  18  ft.  8  in.  +  2.  7.  19  Ib.  2  oz.  +  6. 

2.  19  ft.  8  in.  +  2.  8.  22  Ib.  5  oz.  +  7. 

3.  22  ft.  3  in.  +  3.  9.  17  bu.  2  pk.  +  8. 

4.  34  ft.  8  in.  +  4.  10.  37  bu.  £  pk.  -=-  9. 

5.  31  yd.  4  in.  +  5.  11.  2  ft.  6  in.  +  1  ft.  3  in. 

6.  26  rd.  3£  ft.  +  5.  12.  2  ft.  8  in.  -5-  1  ft.  4  in. 

13.  If  the  perimeter  of  an  equilateral  triangle  is  4  ft.  9  in., 
-how  long  is  each  side  ? 

14.  If  the  perimeter  of  a  square  is  6  ft.  4  in.,  how  long  is 
each  side  ? 

15.  A  box  is  2  ft.  3  in.  long  and  9  in.  wide.    Its  length  is 
how  many  times  its  width  ? 

16.  There  being  16  ft.  6  in.  in  a  rod,  how  many  rods  in 
33  ft.  ?  in  49  ft.  6  in.  ?  in  66  ft.  ?  in  82  ft.  6  in.  ?  in  99  ft.  ? 
in  115  ft.  6  in.  ?    in  132  ft.  ? 


180  FUNDAMENTAL  OPERATIONS 

27.  Review.   Trade  Discount 

When  a  bill  of  goods  listed  at  $100  is  discounted  at  10%,  20%,  the 
10%  is  first  deducted,  leaving  $90,  and  20%  of  $90  is  then  deducted, 
leaving  $72.  Instead  of  taking  10%,  we  may  take  90%  at  once,  and 
instead  of  taking  off  20%  we  may  take  80%  at  once. 

Find  the  cost  of  goods  listed  as  follows,  less  the  discount : 

1.  $500,  5%,  7.  $600,  16|%,  4%. 

2.  $800,  6%.  8.  $900,  33^%,  10%. 

3.  $300,  J  off.  9.  $1500,  20%,  10%. 

4.  $600,  £  off.  10.  $1000,  20%,  10%. 

5.  $200,  10%.  11.  $2000,  20%,  2%. 

6.  $750,  2%.  12.  $5000,  20%.  5%. 

13.  What  is  the  discount  on  $650  at  5%  ? 

14.  How  much  will  $1000  worth  of  hardware  cost  at 
20%  and  10%  discount? 

28.  Review.   Trade  Discount 

Find  the  cost  of  goods  listed  as  follows,  less  the  discount : 

1.  $250,  4%,  10%.  5.  $3000,  33^%,  10%. 

2.  $100,  10%,  5%.  6.  $6000,  16§%,  10%. 

3.  $300,  10%,  1%.  7.  $4000,  12^%,  10%. 

4.  $800,  12£%,  10%.  8.  $5000,  2%,  1%. 

9.  How  much  will  goods  cost  if  marked  $1000  and  sold 
at  a  discount  of  1,  \  ? 

10.  A  dealer  buys  $1200  worth  of  watches  subject  to  a 
discount  of  6%  for  cash.    How  much  does  he  gain  by  taking 
the  discount  ?    How  much  does  he  pay  for  the  watches  ? 

11.  A  dealer  can  buy  $5000  worth  of  goods  on  60  da. 
credit,  or  he  can  get  a  discount  of  10%  for  cash.    How 
much  is  the  discount?    What  is  the  net  cost  if  he  pays 
for  them  immediately  ? 


DIVISION  181 

29.   Division  of  Common  Fractions 

1.  i-2.  6.H-10.  11.  8-f*.  16.10-*-$. 

2.  f-*-3.  7.  T&-5-4.  12.  9-f.  17.  f  -  $ . 

3.  l-s-4.  8.  M-^10-  13-  6-s-f.  18.  f-f. 

4.  g-s-4.  9.  3-£.  14.   8-|.  19.  |  - 1. 

5.  H  +  5-  10-  6^-|-  15-  9-^-1-  20.   f-f. 

21.  How  many  sixths  of  a  mile  are  there  in  §  mi.? 

22.  If,  in  making  a  drawing  to  scale,  we  have  to  divide 
|  in.  into  6  equal  parts,  what  is  the  length  of  each  part  ? 

23.  In  drawing  a  map  it  becomes  necessary  to  divide  £  in. 
into  10  equal  parts.    What  is  the  length  of  each  part  ? 

24.  In  planning  some  trimming  a  girl  needs  to  divide 
|  yd.  into  6  equal  parts.    What  is  the  length  of  each  part  ? 

25.  A  man  has  to  walk  |  mi.  to  his  work.    How  much 
farther  must  he  walk  when  he  has  walked  i  of  the  way  ? 

30.    Division  of  Mixed  Numbers 


1. 

f  - 

=-5. 

6. 

S-T  -J- 

°s  • 

9. 

11. 

7-2J. 

16. 

2. 

2* 

-7-  5. 

7. 

43  _._ 
^s  • 

5. 

12. 

11 

— 

30 
Tf, 

17. 

3. 

3| 

.  Q 

~T~  O. 

8. 

43  _i_ 

7. 

13. 

f  - 

H 

. 

18. 

4. 

3| 

—  5. 

9. 

5  —  | 

14. 

4£ 

— 

n- 

19. 

5. 

4i 

-3. 

10. 

5  —  2 

15. 

41 

-:- 

20. 

21.  If  I  divide  3|  in.  into  5  equal  parts,  what  is  the 
length  of  each  part? 

22.  If  the  perimeter  of  an  equilateral  triangle  is  25^  in., 
what  is  the  length  of  each  side  ? 

23.  A  room  is  11  ft.  3  in.  or  3|  yd.  wide.    How  many 
breadths  of  carpet,  each  27  in.  or  |  yd.  wide,  will  it  take 
to  cover  it? 

24.  Wall  paper  is  \  yd.  wide.    How  many  strips  will  it 
take  to  cover  a  space  5^  yd.  wide  ?    to  cover  a  space  15£-  yd. 
wide? 


182  FUNDAMENTAL  OPERATIONS 

31.    Simple  Accounts 

1.  A  man's  receipts  in  one  day  are  $10,  $2.50,  $3.50, 
$7,  $2.    What  is  the  total  ? 

2.  His  expenses  have  been  $3,  $7,  $2.75,  $1.75,  $5.50. 
What  is  the  total  ? 

3.  By  how  much  do  his  receipts  exceed  his  expenses  ? 

4.  If  he  began  last  week  with  cash  on  hand  amounting 
to  $125,  and  his  receipts  were  $150  and  his  expenses  $110, 
what  was  his  cash  on  hand  at  the  end  of  the  week  ? 

5.  If  his  average  receipts  for  each  of  3  days  are  $25 
and  his  average  expenses  are  $16,  how  much  are  his  net 
receipts  for  the  three  days  ? 

6.  If  he  began  last  year  with  cash  on  hand  amounting  to 
$500,  and  if  his  receipts  were  $7450  and  his  total  expenses 
were  $5200,  how  much  had  he  at  the  end  of  the  year  ? 

32.  Review 

1.  A  fruit  grower  has  2000  trees  that  he  sprays  twice  in 
a  season,  using  5  gal.  to  a  tree  each  time.    Allowing  20/ 
per  100  gal.  for  the  Paris  green,  what  will  this  cost  for  all 
the  trees  ? 

2.  In  making  15  Ib.  of  grafting  wax  the  weight  of  the 
resin  is  60%  of  the  total  weight.    How  many  pounds  of 
resin  are  used? 

3.  A  farmer  needs  500  Ib.  of  nitrate  of  soda  in  making  a 
fertilizer.    How  much  will  this  cost  at  $52  a  ton  ? 

4.  In  shipping  peaches  a  fruit  grower  used  a  crate 
8"  x  12£"  x  22".    How  many  cubic  inches  in  each  crate  ? 
How  many  cubic  inches  in  10  crates  ? 

5.  A  Florida  fruit  grower  had  11  acres  of  pineapples.  He 
sold  the  pineapples  and  averaged  $450  to  an  acre.    How 
much  did  he  receive  ? 


RATIO  183 

33.    Separating  Numbers 

Separate  into  two  parts  having  the  given  ratio  : 

1.  27,  1:2.  7.  27,  4 :  5.  13.  $180,  1 :  2. 

2.  36,  1:2.  8.  36,  4 :  5.  14.  $200,  2  :  3. 

3.  51,1:2.  9.  81,4:5.  15.   $140,3:4. 

4.  25,2:3.  10.  26,5:8.  16.  $270,4:5. 
5.35,2:3.  11.28,5:9.  17.  $330,  4:7. 
6.  75,  2  :  3.  12.  30,  3 :  7.  18.  $240,  5 :  7. 

19.  If  we  divide  44/  between  two  boys  in  the  ratio  of  5 
to  6,  how  much  does  each  receive  ? 

20.  If  we  divide  1000  ft.  of  kite  string  in  the  ratio  of  2  to 
3,  how  long  is  each  part  ? 

21.  If  we  divide  57  acres  in  the  ratio  of  9  : 10,  how  many 
acres  are  there  in  each  part  ? 

34.    Partners 

Divide  between  two  partners  in  the  ratio  specified  : 

1.  $3500,  ratio  of  2  to  3.  5.  $3300,  ratio  of  4  to  7. 

2.  $6300,  ratio  of  4  to  5.  6.  $7000,  ratio  of  3  to  7. 

3.  $2200,  ratio  of  5  to  6.  7.  $3500,  ratio  of  2  to  5. 

4.  $3600,  ratio  of  5  to  7.  8.  $2600,  ratio  of  5  to  8. 
9.  Divide  the  sum  of  $900  and  $400  in  the  ratio  of  5  to  8. 

10.  If  the  ratio  of  gravel  to  clay  in  a  load  (cubic  yard) 
of  earth  is  4  :  5,  how  many  cubic  feet  are  there  of  each  ?     • 

11.  If  two  farmers  together  pay  $70  irrigation  taxes,  and 
one  has  150  acres  and  the  other  200  acres,  what  is  the  share 
that  each  should  pay  ? 

12.  If  the  income  from  a  partnership  was  $2250  last 
month,  and  the  expenses  were  $1000,  and  the  balance  was 
divided  equally  between  two  partners,  what  was  the  share 
of  each  ? 


184  .  EXCHANGE 

II.   EXCHANGE 
35.   Bank  Drafts 

Find  the  cost  of  drafts  for  the  following  amounts  at  the 
given  premium  or  discount : 

1.  $100,  0.1%  premium.  6.  $2500,  £%  premium. 

2.  $200,  0.1%  premium.  7.  $300,  0.1%  discount. 

3.  $400,  0.1%  premium.  8.  $500,  0.1%  discount. 

4.  $750,  0.1%  premium.  9.  $1000,  0.1%  discount. 

5.  $5000,  £%  premium.  10.  $5000,  0.1%  discount. 

11.  $2500,  40^  premium  per  $1000. 

12.  $4000,  75/  premium  per  $1000. 

13.  $5000,  50/  discount  per  $1000. 

14.  A  draft  for  $3000  cost  a  man  $3001.50.  How  much 
premium  did  he  pay  per  $1000  ? 

36.    Commercial  Drafts 

Drafts  for  the  following  amounts  are  drawn  by  wholesale 
merchants  upon  their  customers.  The  banks  charge  the  given 
per  cents  for  collection.  Find  the  net  proceeds  : 

1.  $100,  0.1%.        6.  $1000,  0.1%.      11.  $250,  0.3%. 

2.  $200,  0.1%.        7.  $200,  0.2%.        12.  $1000,  0.3%. 

3.  $500,0.1%.        8.  $300,0.2%.        13.  $4000,4%. 

4.  $600,  0.1%.        9.  $2000,  0.2%.      14.  $6000,  TV%. 

5.  $800,  0.1%.      10.  $100,  0.3%.        15.  $8000,  TV%. 

16.  $750,  40X  per  $1000.        19.  $1500,  80/  per  $1000. 

17.  $800,  50/  per  $1000.        20.  $2500,  80/  per  $1000. 

18.  $7500,  80X  per  $1000.      21.  $3000,  75/  per  $1000. 
22.  W.  H.  Jackson  owes  $500,  less  20%,  for  some  goods 

bought  of  The  Koberts  Manufacturing  Co.  The  company 
draws  on  him  for  the  amount  due.  What  is  the  net  amount 
received,  less  0.1%  for  collecting  ? 


ENGLISH  MONEY  185 

37.  English  Money 
Express  as  pence: 

1.  Is.         3.  6s.  5.  20s.          7.  £1.          9.  2s.  6d. 

2.  4s.         4.  10s.         6.  40s.          8.  £2.         10.  10s.  8d. 

Express  as  shillings  : 

11.  24d.     12.  GOd.      13.  240d.      14.  £3.         15.  £4  10s. 

Express  as  pounds,  or  as  pounds  and  shillings  : 

16.  40s.      17.  80s.       18.  480d.      19.  30s.        20.  50s. 

Perform  the  operations  indicated  : 

21.  £10  12s.  +  £5  8s.        25.  2  x  £2  10s. 

22.  £8  15s.  +  £9  15s.        26.  4  x  £2  5s  3d. 

23.  £15  10s.  -  £4  15s.        27.  £5  4s.  -=-  4. 

24.  £24  4s.  -  £3  6s.         28.  £5  -*•  £2  10s. 

38.  English  Money 

Taking  Id.  as  2ft,  express  in  United  States  money  : 
1.  7d.         2.  9d.          3.  17d.       4.  37d.          5.  240d. 

Taking  2ft  as  Id.,  express  in  English  money  : 
6.  50<.       7.  70/.        8.  $1.         9.  10/.        10.  25/. 


Taking  Is.  as  24fi>  express  in  United  States  money  : 
11.  2s.        12.  6s.         13.  5s.        14.  10s.         15.  15s. 


Taking  %4fi  as  ls->  express  in  English  money  : 

16.  72/.      17.  $1.20.      18.  36/.      19.  $1.      20.  $1.50. 

Taking  £1  as  $4-87,  express  in  United  States  money  : 
21.  £10.      22.  £100.     23.  £2.      24.  £1000.     25.  10s. 

Taking  $5  as  £1,  express  in  English  money  : 

26.  $25.     27.  $75.     28.  $125.     29.  $350.     30.  $575. 


186  EXCHANGE 

39.  French  Money 

Express  as  centimes : 
1.  2fr.        2.  7fr.         3.  65  fr.       4.  250  fr.     5.  5fr.  lOc. 

Express  as  francs  : 
6.  200  c.      7.  500  c.      8.  700  c.      9.  900  c.    10.  2000  c. 

Express  as  francs  and  centimes : 

11.  250  c.    12.  725  c.    13.  645  c.    14.  875  c.    15.  2550  c. 

Perform  the  operations  indicated : 

16.  7  fr.  60  c.  +  6  fr.  40  c.  21.  25  fr.  50  c.  -  4  fr.  75  c. 

17.  8  fr.  90  c.  +  7  fr.  60  c.  22.  2  x  25  fr.  50  c. 

18.  8.50  f r.  +  1.50  fr.  +  5  fr.       23.  5  x  20  fr.  40  c. 

19.  7.60  f  r.  +  40  c.  +  12  fr.          24.  35  fr.  75  c.  -=-  5. 

20.  15  fr.  50  c.  -  5  f  r.  50  c.          25.  31  f  r.  20  c.  --  3. 

40.  French  Money 

Taking  the  common  equivalent,  1  fr.  =  20  fl,  or  $j,  express 
in  United  States  money  : 

1.  7  f  r.        3.  15  f  r.       5.  250  f  r.     7.  72  fr.          9.  130  fr. 

2.  35  f  r.      4.  75  fr.       6.  18  fr.       8.  36  fr.        10.  650  fr. 

Taking  the  more  exact  equivalent,  1  fr.  =  19.3  fi,  express 
in  United  States  money : 

11.  10  fr.    12.  5  fr.       13.  20  fr.     14.  100  fr.      15.  1000  fr. 

Taking  $1  =  5  fr.,  express  in  French  money  : 

16.  $4.       18.  $2.50.   20.  $50.      22.  $3.50.      24.  $2.25. 

17.  $13.     19.  $7.50.   21.  $2.80.  23.  $1.25.      25.  $3.75. 

Taking  the  more  exact  equivalent,  $1  =5.18  fr.,  express  in 
French  money : 

26.  $10.     27.  $100.     28.  $2.        29.  $20.         30.  $1000. 


GERMAN  MONEY  187 

41.  German  Money 
Express  as  pfennigs : 

1.  1  M.      2.  7M.      3.  2^M.      4.  3M.  60 pf.      5.  150  pf. 

Express  as  marks : 
6.  200  pf.    7.  400  pf.    8.  900  pf.    9. 1200  pf.    10.  7500  pf. 

Express  as  marks  and  pfennigs : 

11.  125  pf.  12.  230  pf.  13.  350  pf.  14.  640  pf.  15.  1275  pf. 

Perform  the  operations  indicated: 

16.  7  M.  80  pf.  +  2  M.  20  pf.  21.  3  x  41  M.  25  pf. 

17.  25  M.  50  pf.  +  30  M.  75  pf.       .  22.  5  x  40  M.  40  pf. 

18.  32  M.  75  pf.  -  1  M.  60  pf.  23.  1  of  40  M.  75  pf. 

19.  75  M.  20  pf .  -  4  M.  70  pf .  24.  f  of  80  M.  40  pf . 

20.  18  M.  10  pf .  -  9  M.  80  pf.  25.  44  M.  22  pf .  --  6. 

42.  German  Money 

Taking  the  common  equivalent,  1  M.  =  24? >   express  in 
United  States  money : 

1.  2M.  3.  5M.     5.  5M.50pf.  7.  11  M.     9.  25  M. 

2.  3M.  4.  5^M.  6.  10  M.  8.  20  M.   10.  10  M.  50  pf. 

Taking  the  more  exact  equivalent,  1  M.  =  23.8 'fi,  express 
in  United  States  money : 

11.  10  M.     12.  20  M.     13.  2M.      14.  100  M.     15.  1000  M. 

Taking  $1  as  equal  to  4  M-  %0  pf.,  express  in  U.  S.  money  : 
16.  8M.40pf.   17.  21M.    18.  42M.    19.  420M.    20.  840M. 

Taking  the  rough  approximation,  $1  =  4  M.,  express  in 
United  States  money : 

21.  100  M.    23.  60  M.  25.  200  M.   27.  360  M.   29.  1000  M. 

22.  240  M.    24.  80  M.   26.  480  M.   28.  840  M.   30.  4000  M. 


188  EXCHANGE 

43.  Foreign  Exchange 

Exchange  being  $4-84  to  the  pound,  find  the  cost  of  drafts 
for  the  folloiving  amounts : 

1.  £2.        2.  £5.        3.  £10.        4.  £100.          5.  £1 10s. 

Also  for  the  following,  exchange  being  $4-80  to  £1 : 
6.  £5.        7.  £25.      8.  £100.      9.  £1000.      10.  £1 10s. 

At  $4-?8  to  £l,find  the  face  of  a  draft  costing : 

11.  $47.80.    12.1478.    13.  $4780.    14.  $2.39.   15.  $23.90. 

16.  If  an  importer  buys  goods  in  London  to  the  value 
of  £1000,  how  much  will  a  draft  for  this  amount  cost, 
exchange  being  quoted  at  4.83^  ? 

17.  An  importer  paid  $482.25  for  a  draft  on  London, 
exchange  being  quoted  at  4.82|.   What  was  the  face  ? 

44.  Foreign  Exchange 

Exchange  being  94^0  to  4  M.,  find  the  cost  of  drafts  for  : 

1.  40  M.  3.  400  M.  5.  4000  M.         7.  20  M. 

2.  80  M.  4.  800  M.  6.  8000  M.        8.  200  M. 

Exchange  being  240  to  1  M.,  find  the  cost  of  drafts  for : 

9.  10  M.          11.  200  M.         13.  300  M.         15.  500  M. 
10.  100  M.        12.  2000  M.       14.  3000  M.       16.  5000  M. 

Exchange  being  5.14  fr.  to  $1,  find  the  cost  of  drafts  for  : 

17.  51  fr.  40  c.  19.  5140  fr.       21.  257  fr.         23.  15.42  fr. 

18.  514  fr.         20.  51,400  fr.    22.  2570  fr.       24.  1542  fr. 

Exchange  being  19. 7 '/  to  1  fr.,  find  the  cost  of  drafts  for: 

25.  100  fr.         27.  1000  fr.        29.  10,000  fr.    31.  10  fr. 

26.  200  fr.         28.  2000  fr.       30.  20,000  fr.    32.  30  fr. 


METRIC  SYSTEM  189 

III.    METRIC  SYSTEM 

45.  Length 
Express  as  millimeters : 

1.  2  cm.      2.  50  cm.      3.  4.25  m.    4.  3.8  cm.      5.  1  km. 

Express  as  centimeters  : 
6.  4  m.        7.  20  m.        8.  20mm.    9.  100  m.     10.  3^  m. 

Express  as  decimeters  : 
11.  2  m.      12.  50  cm.    13.  60  m.     14.  1  km.      15.  500  mm. 

Express  as  meters  : 
16.2km.    17.3.5km.   18.70dm.   19.600cm.   20.7000mm. 

Express  as  kilometers  : 
21.  5000  m.     22.  2500  m.     23.  2575  m.      24.  600,000  cm. 

46.  Length 

Taking  1  cm.  =  0.4  in.,  express  as  inches: 
1.10cm.       2.2cm.        3.20cm.      4.2.5cm.       5.5cm. 

Taking  1  dm.  =  3.9  in.,  express  as  inches : 
6.  2  dm.        7.  10  dm.       8.  5  dm.        9.  3  dm.       10.  4  dm. 

Taking  1  m.  =  39.37  in.,  express  as  inches  : 
11.  10  m.      12.  0.1  m.     13.  100m.     14.  0.01m.     15.  1  km. 

Taking  1  m.  =  <?|  ft.,  express  as  feet  : 

16.  10  m.      18.  400  m.    20.  72  m.      22.  15  m.       24.  25  m. 

17.  4  m.         19.  8  m.        21.  20  m.      23.  60  m.       25.  1  km. 

Taking  1  km.  =  0.6  mi.,  express  as  miles  : 
26.  10  km.     27.  2  km.      28.  20  km.    29.  5|  km.     30.  15  km. 


190  METRIC  SYSTEM 

47.   Square  Measure 
Express  as  square  meters: 
1.  1  sq.  km.      2.  3  sq.  km.     3.  5^  sq.  km.     4.  200  sq.  dm. 

Express  as  hektares  (square  Jiektometers)  : 
5.  20,000  sq.  m.    6.  2  sq.  km.    7.  5  sq.  km.     8.  10  sq.  km. 

Express  as  square  meters: 
9.  6  square  dekameters.  10.  3  square  hektometers. 

Taking  1  ha.  =  2j  A.,  express  as  hektares  : 

11.  7£  A.     12.  10  A.       13.  12^  A.     14.  15  A.     15.  250  A. 

Express  as  acres : 

16.  2  ha.     17.  10  ha.     18.  5  ha.        19.  8  ha.      20.  80  ha. 

/ 

48.   Review 

1.  A  certain  tower  is  100  m.  high.    How  many  feet  ? 

2.  A  certain  distance  is  200  km.    How  many  miles  ? 

3.  A  certain  mountain  is  4000  m.  high.  How  many  feet  ? 

4.  If  a  train  is  traveling  2  km.  a  minute,  what  is  its  rate 
in  miles  ? 

5.  If  a  train  is  traveling  0.9  mi.  a  minute,  what  is  its 
rate  in  kilometers  ? 

6.  Taking  the  distance  across  the  Atlantic  as   about 
3000  mi.,  how  many  kilometers  is  this  ? 

7.  Taking  the  distance  around  the  world  at  a  certain 
latitude  as  40,000  km.,  how  many  miles  is  this  ? 

Taking  1  ha.  =  2.47  A.,  express  as  acres : 

8.  10  ha.        10.  2  ha.         12.  200  ha.        14.  10,000  ha. 

9.  100  ha.      11.  20  ha.      13.  2000  ha.      15.  20,000  ha. 


CUBIC  MEASURE 


191 


49.   Cubic  Measure 

Express  as  cubic  meters  : 

1.  2.5  st.  3.  4000  cu.  dm.       5.  35  st. 

2.  2000  cu.  dm.       4.  10,000  cu.  dm.    6.  625  st. 

Express  as  cubic  decimeters: 

7.  Scu.m.  9.  7000  cu.  cm. 

8.  15  st.  10.  27  cu.  m. 


11.  6jst. 

12.  50,000  cu.  cm. 


Express  as  cubic  centimeters  : 

13.  1  cu.  m.  15.  1  cu.  dm. 

14.  50  cu.  m.          16.  15  cu.  dm. 

Express  as  cubic  kilometers  : 
19.  3000  cubic  hektometers. 


17.  2000  cu.  mm. 

18.  10,000  cu.  mm. 


20.  4,000,000,000  cu.  m. 


50.   Review 

1.  A  pile  of  wood  is  1  m.  x  2  m.  x  8  m.    How  many  steres 
does  it  contain  ? 

2.  A  tank  is  5  m.  x  2  m.  x  3  m.   How  many  cubic  meters 
does  it  contain  ? 

3.  A  box  is  2  m.  long,  1.5  m.  wide,  and  50  cm.  deep.    How 
many  cubic  meters  does  it  contain  ? 

4.  A  room  is  6  m.  long,  5  m.  wide,  and  3  m.  high.    How 
many  steres  of  wood  would  it  take  to  fill  it  ? 

5.  An  aquarium  is  50  cm.  long,  25  cm.  wide,  and  20  cm. 
deep.    How  many  cubic  centimeters  does  it  contain  ? 

6.  A  chest  is  1.5  m.  long,  0.5  m.  wide,  and  0.2  m.  deep. 
What  part  of  a  cubic  meter  does  it  contain  ? 

7.  A  block  of  stone  is  2  m.  long,  0.25  m.  thick,  and  0.5  m. 
wide.    What  part  of  a  cubic  meter  does  it  contain?    How 
many  cubic  decimeters  ? 


192  METRIC  SYSTEM 

51.  Weight 

Express  as  grams  : 

1.  2  kg.  4.  25  kg.          7.  0.3  kg.         10.  275  eg. 

2.  7  kg.  5.  635  kg.        8.  0.45  kg.       11.  680  eg. 

3.  1.5  kg.         6.  47.5  kg.       9.  150  eg.         12.  7250  mg. 

Express  as  centigrams : 

13.  250  g.        14.  7  kg.          15.  15  kg.          16.  7500  mg. 

Express  as  milligrams  : 

17.  50  g.          18.  2J  g.  19.  5.4  g.  20.  65  eg. 

Express  as  Idlos  (kilograms): 

21.  2000  g.   23.  5250  g.   25.  27,500  g.  27.  25  t. 

22.  6000  g.  24.  7750  g.   26.  30,000  g.  28.  50  t. 

52.  Weight 

1.  If  a  traveler's  trunks  weigh  220  lb.,  how  many  kilos 
do  they  weigh,  allowing  2.2  lb.  to  the  kilo  ? 

2.  If  two  travelers  together  are  allowed  50  kg.  of  free 
baggage,  how  many  pounds  are  they  allowed  ? 

3.  If  1  cu.  m.  of  water  weighs  1  t.,  what  will  be  the 
weight  of  the  water  that  fills  a  tank  3  m.  x  3  m.  x  1.5  m.  ? 

4.  If  granite  is  2.7  times  as  heavy  as  water,  what  will 
0.5  cu.  m.  of  granite  weigh  ? 

5.  If  you  weigh  110  lb.,  how  many  kilograms  do  you 
weigh  ? 

6.  If  two  boys  together  weigh  100  kg.,  how  many  pounds 
do  they  weigh  ? 

7.  A  5-cent  piece  weighs  5  g.   How  many  will  it  take  to 
weigh  half  a  kilo  ?    How  much  will  $5  in  nickels  weigh  ? 
How  much  will  $20  in  nickels  weigh  ? 


CAPACITY  193 

53.  Capacity 

Express  as  liters : 

1.  4  hi.  2.  8i  hi.  3.  75  hi.  4.  6.25  hi. 

Express  as  hektoliters  : 
5.  750  1.          6.  275  1.  7.  625  1.  8.  3500  1. 

Taking  1  1.  =  1  qt.,  express  as  quarts: 
9.  7  hi.  10.  65  hi.  11.  9.5  1.  12.  725  hi. 

Express  as  liters  (cubic  decimeters') : 

13.  9cu.dm.     14.  0.3 cu. dm.     15.  leu. m.     16.  O.Scu.m. 

17.  Knowing  that  1  1.  of  water  weighs  1  kg.,  what  is 
the  weight  of  35  1.  of  water  ?  of  72.25  1. ?  of  67.5  hi.?  of 
10  cu.  m.  ? 

54.  Review 

1.  Taking  alcohol  as  0.83  times  as  heavy  as  water,  how 
many  kilos  does  10  1.  of  alcohol  weigh  ? 

2.  Taking  gold  as  19.3  times  as  heavy  as  water,  and 
1  cu.  cm.  of  water  weighing  1  g.,  how  much  does  10  cu.  cm. 
of  gold  weigh  ? 

3.  Taking  silver  as  10.5  times  as  heavy  as  water,  how 
much  does  2  cu.  cm.  of  silver  weigh  ? 

4.  A  tank  is  4  m.  long,  3  m.  wide,  and  3  m.  deep.    How 
many  metric  tons  of  water  will  it  take  to  fill  it  ?    How  many 
kilos? 

5.  Taking  a  quart  as  nearly  the  same  as  a  liter,  how 
many  kilos  will  1  gal.  ef  water  weigh  ?    10  gal.  of  water  ? 
How  many  pounds  will  10  gal.  of  water  weigh  ? 

6.  How  much  will  the  water  weigh  that  fills  an  aquarium 
0.5m.  by  0.4m.  by  0.2  m.? 


194  TAXES 

IV.    TAXES 

55.  Duties  on  Imports 

Find  the  duty  on  each  of  tlie  following  invoices  of  goods  at 
the  rate  specified  : 

1.  $200,  25%.         5.  $225,  50%.           9.  $480,  25%. 

2.  $250,  20%.          6.  $300,  35%.         10.  $630,  40%. 

3.  $300,  15%.          7.  $700,  60%.         11.  $660,  15%. 

4.  $600,  40%.         8.  $840,  25%.         12.  $1200,  45%. 

13.  700H)u.  barley,  duty  30/  a  bushel. 

14.  1200  gal.  olive  oil,  duty  50/  a  gallon. 

15.  1600  Ib.  snuff,  duty  55/  a  pound. 

16.  2500  Ib.  tobacco,  duty  $2  a  pound. 

17.  6400  T.  iron  ore,  duty  15^  a  ton. 

18.  3200  bu.  potatoes,  duty  25/  a  bushel 

56.  Duties  on  Imports 

1.  Allowing  $4.80  to  the  pound  sterling,  how  much  more 
does  a  man  have  to  pay  for  English  books  that  cost  £100 
in  London,  on  which  the  duty  is  25%,  than  he  would  if  there 
were  no  duty  ? 

2.  How  much  more  does  a  man  have  to  pay  for  a  painting 
that  cost  $300  in  Paris,  the  duty  being  15%,  than  he  would 
if  there  were  no  duty  ? 

Find  the  duty  on  each  of  the  following  invoices  of  goods  at 
the  rate  specified  : 

3.  $4000  worth  of  automobiles,  45%. 

4.  $800  worth  of  English  books,  25%. 

5.  $200  worth  of  perfumery,  50%. 

6.  $2000  worth  of  musical  instruments,  45%. 

7.  $600  worth  of  paintings,  15%. 

8.  $100  worth  of  earthenware,  25%. 


TAXES  195 

57.  Local  Taxes 

Find  the  tax  on  each  of  the  following  : 

1.  $1000  at  6  mills.  11.  $1000  at  4|  mills. 

2.  $1000  at  4  mills.  12.  $4000  at  4i  mills. 

3.  $3000  at  6  mills.  13.  $8000  at  4£  mills. 

4.  $2000  at  5  mills.  14.  $4000  at  4£  mills. 

5.  $2500  at  4  mills.  15.  $4000  at  6£  mills. 

6.  $7500  at  4  mills.  16.  $8000  at  6£  mills. 

7.  $3400  at  5  mills.  17.  $4000  at  6J  mills. 

8.  $4800  at  5  mills.  18.  $8000  at  6J  mills. 

9.  $1000  at  5£  mills.  19.  $10,000  at  5}  mills. 
10.  $2000  at  5£  mills.  20.  $20,000  at  5|  mills. 

21.  What  is  the  tax  on  $5000  at  8.2  mills? 

22.  What  is  the  tax  on  $4000  worth  of  real  estate  and 
$5000  worth  of  personal  property,  the  tax  rate  being  7  mills  ? 

58.  Local  Taxes 

Given  the  following  assessed  valuations  and  tax  levies,  find 
the  tax  per  dollar  : 

1.  $1,000,000,  $5000.  9.  $4,000,000,  $26,000. 

2.  $2,000,000,  $10,000.  10.  $6,000,000,  $33,000. 

3.  $4,000,000,  $16,000.  11.  $8,000,000,  $42;000. 

4.  $5,000,000,  $20,000.  12.  $7,000,000,  $28,000. 

5.  $3,000,000,  $18,000.  13.  $2,500,000,  $10,000. 

6.  $7,000,000,  $35,000.  14.  $2,300,000,  $11,500. 

7.  $2,000,000,  $11,000.  15.  $3,400,000,  $17,000. 

8.  $4,000,000,  $18,000.  16.  $12,000,000.  $60,000. 

17.  A  city  has  to  raise  $100,000  by  tax.    If  the  assessed 
valuation  is  $10,000,000,  what  is  the  rate  ? 

18.  A  town  has  to  raise  by  tax  $1800  for  one  purpose 
and   $8200   for   another.     The    assessed   valuation   being 
$1,000,000,  what  is  the  rate? 


196  INSURANCE 

V.  INSURANCE 

59.  Fire  Insurance 

Find  the  premiums  on  the  following  policies  at  the  rates 
specified : 

1.  $1000,  1%.        4.  $2000,  \\%.         7.  $2500, 

2.  $1000,  li%.       5.  $2000,  li%.          8.  $3000, 

3.  $1000,  |%.         6.  $2000,  If  %.          9.  $4000,  If  %. 

10.  At  $1.15  per  thousand,  what  is  the  premium  on  a 
$3000  policy  ? 

11.  At  $1.65  per  thousand,  what  is  the  premium  on  a 
$2000  policy  ? 

12.  A  building  worth  $9000  is  insured  for  §  of  its  value 
at  2%.   What  is  the  premium?   What  would  be  the  pre- 
mium if  it  were  insured  for  \  of  its  value  ? 

60.  Fire  Insurance 

Find  the  premiums  on  the  following  policies  at  the  rates 
specified : 

1.  $2250,2%.         4.  $2000,21%.          7.  $4000,  2f%. 

2.  $3750,  2%.         5.  $3200,  2\%.         8.  $8000,  2 

3.  $7500,  2%.         6.  $4800,  2i%.          9.  $2500, 

10.  A  3-year  policy  for  $4000  costs  $90.   What  is  the 
rate  of  premium  per  year? 

11.  A  3-year  policy  for  $5000  costs  $150.    What  is  the 
rate  per  thousand  per  year  ? 

12.  A  man  insured  his  stock  of  goods,  valued  at  $16,000, 
for  I  of  its  value,  at  $2  per  thousand.    What  was  the 
premium  ? 

13.  A  store  worth  $4000,  containing  $12,000  worth  of 
goods,  is  insured  for  f  of  the  value  of  the  store  and  goods  at 

What  is  the  premium  ? 


INSURANCE  197 

61.  Life  Insurance 

Find  the  premiums  on  the  following  policies,  the  premiums 
on  $1000  being  given  : 

1.  $3000,  $27.  5.  $2500,  $25.  9.  $2500,  $28. 

2.  $4000,  $26.  6.  $3500,  $24.  10.  $8000,  $28. 

3.  $5000,  $23.  7.  $8000,  $25.  11.  $2000,  $25.50. 

4.  $2500,  $24.  8.  $7000,  $25.  12.  $4000,  $25.25. 

13.  What  premium  must  a  man  pay  on  an  endowment 
policy  for  $5000  at  $104.20  per  thousand? 

14.  A  man  takes  out  a  $5000  20-payment  policy  at  $28 
per  thousand.    What  does  he  pay  each  year  ?   in  20  years  ? 

15.  A  man  takes  out  a  $15,000  20-payment  policy  at 
$30  per  thousand.    What  does  he  pay  each  year  ?    What 
does  he  pay  in  20  years  ? 

62.  Life  Insurance 

Find  the  premiums  on  the  following  policies,  the  premiums 
on  $1000  being  given: 

1.  $4000,  $27.  5.  $8000,  $26.         9.  $5000,  $26.40. 

2.  $3000,  $28.  6.  $6000,  $25.  10.  $4000,  $25.20. 

3.  $6000,  $29.  7.  $15,000,  $28.  11.  $2500,  $28.80. 

4.  $7500,  $30.  8.  $16,000,  $25.  12.  $25,000,  $32.40. 

13.  A  man  takes  out  a  $2000  policy  in  one  company  at 
$28  a  thousand,  and  a  $3000  policy  in  another  at  $25  a 
thousand.    What  are  his  annual  premiums  ? 

14.  A  man  takes  out  a  policy  for  $8000,  on  which  he 
pays  an  annual  premium  of  $240.    What  is  the  premium 
per  thousand  ? 

15.  A  man  takes  out  a  policy  on  which  he  pays  an  annual 
premium  of  $84,  the  premium  per  thousand  being 
What  is  the  face  of  the  policy  ? 


198  CORPORATIONS 

VI.   CORPORATIONS 
63.    Shares 

At  $100  a  share,  find  the  number  of  shares  in  companies 
with  the  following  capitals: 

1.  $50,000.    2.  $75,000.    3.  $125,000.     4.  $5,000,000. 

Also  with  the  following  capitals  at  $50  a  share: 
5.  $25,000.     6.  $30,000.     7.  $75,000.       8.  $2,000,000. 

Also  ivith  the  following  capitals  at  $25  a  share: 

9.  $50,000.  10.  $60,000.  11.  $35,000.     12.  $1,000,000. 
13.  If  a  man  owns  300  shares  of  stock  worth  $112  a  share, 
what  is  the  value  of  his  stock  ? 

64.   Dividends 

Allowing  $100  to  a  share  in  this  exercise,  find  the  dividends 
due  to  holders  of  the  following  number  of  shares  at  the  rates 
specified: 

1.  10,  4%.     4.  30,  6%.        7.  75,  5%.        10.  200,  8%. 

2.  20,  5%.      5.  40,  5£%.      8.  80,  7%.         11.  250,  8%. 

3.  25,  8%.      6.  60,  4J%.      9.  100,  1\%.    12.  600,  5%. 

13.  A  company  with  $200,000  capital  divides  $10,000  in 
dividends.    What  is  the  rate  of  dividend  ? 

14.  A  company  with  $75,000  capital  declares  a  4<%  divi- 
dend.   How  much  does  it  divide  in  dividends  ? 

15.  A  company  with  $50,000.000  capital  declares  a  6% 
dividend.    How  much  does  it  divide  in  dividends  ? 

16.  A  company  divides  $40,000  in  dividends,  and  stock- 
holders receive  8%  on  their  stock.   What  is  the  capital  of 
the  company  ? 


BUYING  AND  SELLING  STOCKS  199 

65.  Buying  Stocks 

Following  the  business  custom,  add  |  to  the  following  newspaper 
quotations,  as  brokerage,  in  buying  stocks.  Thus  10  shares,  of  $100 
each,  quoted  at  91|  cost  10  x  §92,  or  §920. 

Find  the  cost  of  10  shares  of  stock  quoted  as  follows  : 

1.  75£.         3.  99f.         5.  72|.  7.  78|.         9.  127f. 

2.  92|.         4.  112$.       6.  83|.  8.  83f.       10.  92f. 

Find  the  cost  of  100  shares  quoted  as  follows  : 

11.  731.       13.  87i.       15.  1431.       17.  85^.       19.  34J. 

12.  82i.       14.  96i.       is.  126|.       18.  7Si.       20.  52f. 

Adding  brokerage  as  above,  find  the  cost  of: 

21.  25  shares  at  79j.  22.  50  shares  at  123$. 

66.  Selling  Stocks 

Following  the  business  custom,  subtract  |  from  the  following  quo- 
tations, as  brokerage,  in  selling  stocks.  Thus  10  shares,  of  $100  each, 
quoted  at  91|  will  bring  10  x  $91|,  or  §917.50. 

Find  the  amount  received  from  the  sale  of  10  shares  of 
stock  quoted  as  follows : 

1.  92f         3.  85|.         5.  83|.  7.  73|.         9.  150|. 

2.  96f         4.  127|.       6.  67f.  8.  42f.        10.  37|. 

Also  from  100  shares  quoted  as  follows  : 

11.  87],       13.  82i.       15.  73j.         17.  85|.       19.  130|. 

12.  75i.       14.  1251.     16.  96^.         18.  98|.       20.  88|. 

21.  What  will  a  man  receive  from  selling  1000  shares  of 
stock  when  it  is  quoted  at  94£  ? 

22.  What  will  a  man  gain  by  buying  100  shares  of  stock 
quoted  at  92|,  and  selling  when  quoted  at  101|  ? 


200  CORPORATIONS 

67.   Bonds 

Find  the  income  on  bonds  of  the  following  amounts,  at  the 
rates  specified: 

1.  $7000,  5%.  5.  $4000,  4^%.  9.  $15,000,  5%. 

2.  $7500,5%.  6.  $6000,4^%.  10.  $25,000,4%. 

3.  $8000,  4%.  7.  $9000,  3%.  11.  $80,000,  4£%. 

4.  $8500,  4%.  8.  $8000,  3J%.  12.  $40,000, 


To  find  the  cost  of  bonds,  add  £  to  the  quotation,  as  with  stocks,  to 
pay  the  broker  for  buying.  Thus,  §2000  in  bonds  quoted  at  103|  cost 
20  X  §103.75,  or  §2075. 

Find  the  cost  of  bonds  for  the  following  amounts  : 

13.  $2000,  103|.     16.  $4000,  102J.     19.  $6000,  100J. 

14.  $3000,  101  f.     17.  $8000,  110.       20.  $10,000,  102|. 

15.  $7500,  99f       18.  $5000,  109f    21.  $12,000,  109J. 

68.    Stocks  and  Bonds 
Take  the  par  value  of  one  share  of  stock  as  §100. 

1.  What  is  the  income  on  $8000  of  5%  stock? 

2.  What  is  the  income  on  50  shares  of  stock  paying  4%  ? 

3.  What  is  the  income  on  100  shares  of  stock  paying 


4.  If  a   man  buys  100   shares  of  stock  when  quoted 
at  96|  and  sells  it  when  quoted  at  98^,  how  much  does 
he  gain  ? 

5.  If  a  man  buys  a  $1000  bond  when  quoted  at  102| 
and  sells  it  when  quoted  at  100^,  how  much  does  he  lose  ? 

6.  If  an  investor  receives  $6  on  every  $120  invested, 
what  is   his  rate  of  income  ?    If  a  purchaser  buys  a  6% 
stock  when  quoted  at  119|,  what  is  his  rate  of  income  ? 

7.  If  an  investor  buys  a  7%  stock  when  quoted  at  139|, 
what  is  his  rate  of  income  ?    (Tf  ^  =  what  per  cent  ?) 


STOCKS  AND  BONDS  201 

69.  Review 

1.  A  man  buys  300  shares  of  Pennsylvania  R.  R.  stock 
when  quoted  at  134|,  and  sells  it  when  quoted  at  135|. 
Does  he  gain  or  lose  ?    (Remember  the  £  for  brokerage.) 

2.  An  investor  buys  50  shares  of  Union  Pacific  stock 
when  quoted  at  112|,  and  sells  it  when  quoted  at  114f. 
How  much  does  he  gain  on  a  share  ?   on  the  50  shares  ? 

3.  An  investor  buys  100  shares  of  Illinois  Central  stock 
when  quoted  at  132f,  and  sells  it  when  quoted  at  130^. 
How  much  does  he  lose  on  a  share  ?    on  the  100  shares  ? 

4.  If  a  man  receives  $5  on  every  $125  invested,  what 
per  cent  does  he  receive?    If  he  buys  a  5%  stock  when 
quoted  at  124$,  what  per  cent  does  he  receive  ? 

5.  If  an  investor  buys  an  8%  stock  when  quoted  at  $159  £, 
what  per  cent  does  he  receive  ?    (Tf  ^  is  what  per  cent  ?) 

70.  Review 

1.  How  much  does  a  grocer  pay  a  bottle  for  olives  that 
cost  him  $14.40  a  gross  ? 

2.  How  much  does  a  grocer  pay  a  bottle  for  mustard  that 
costs  him  $1.80  a  dozen  ? 

3.  If  a  grocer  pays  $12  for  300  Ib.  of  sugar,  how  much 
does  it  cost  him  a  pound  ? 

4.  If  a  grocer  buys  soap  at  $3  a  box  of  GO  cakes,  what 
must  be  the  selling  price  per  cake  to  allow  him  to  make 
20%  ?  to  make  40%  ? 

5.  If  a  grocer  buys  canned  fruit  at  $1.92  a  dozen,  what 
does  he  pay  per  can  ? 

6.  If  a  grocer  buys  25  Ib.  of  honey  for  $3.75,  what  does 
he  pay  a  pound  ? 

7.  At  what  price  per  pound  must  the  grocer  sell   the 
honey  mentioned  in  Ex.  6  in  order  to  make 


202  POWERS  AND  ROOTS 

VII.    POWERS  AND  ROOTS 

71.   Powers 

22  =  2x2=4;  23  =  2x2x2  =  8;  2*  =  22  x  22  =  4  x  4  =  16 ;  28  =  22 
x  23  =  4  x  8  =  32  ;  26  =  23  x  23  =  8  x  8  =  64 ;  and  so  on. 

Find  the  values  of  the  following  : 


1.  32. 

8.  102. 

15.  1002. 

22.  9s. 

29.  104. 

2.  42. 

9.  II2. 

16.  33. 

23.  10s. 

30.  204. 

3.  52. 

10.  122. 

17.  48. 

24.  12». 

31.  25. 

4.  62. 

11.  202. 

18.  58. 

25.  20s. 

32.  35. 

5.  72. 

12.  302. 

19.  6s. 

26.  24. 

33.  26. 

6.  82. 

13.  402. 

20.  73. 

27.  34. 

34.  27. 

7.  92. 

14.  702. 

21.  83. 

28.  54. 

35.  10s. 

36.  Which  is  greater,  2s  or  32  ?   How  much  greater  ? 

37.  Which  is  greater,  24  or  42  ?    How  much  greater  ? 

72.   Squares  and  Cubes 

The  square  of  t  +  u  is  t2  +  2  x  t  x  w  +  w2.   So  132  =  102  +  2  x  10 
x  3  +  32  =  100  +  60  +  9  =  169. 

Square  the  following  : 

1.  11.  3.  14.  5.  31.  7.  1.2.          9.  102. 

2.  12.  4.  21.  6.  1.1.  8.  101.        10.  103. 

Find  the  areas  of  squares  with  sides  as  follows : 

11.  7ft.        12.  0.5  in.     13.  1.2ft.     14.  0.7  in.     15.  2.5yd. 

Find  the  volumes  of  cubes  with  edges  as  follows : 

16.  3  in.        18.  12  in.      20.  10  in.      22.  0.3  in.     24.  20  in. 

17.  0.4  in.     19.  1.2  in.     21.  0.5  in.     23.  0.9  in.     25.  100  in. 
26.  A  field  is  40  rd.  square.    How  many  acres  does  it 

contain  ? 


SQUARE  ROOT  203 

73.  Square  Root 

To  find  the  square  root  of  4900  mentally,  separate  it  into  two  equal 
groups  of  factors,  thus :  4900  =  (10  x  7)  x  (10  x  7)  =  702. 

Find  the  square  roots  of  the  following  : 

1.  i.  4.  25.          7.  36.         10.  900.    •       13.  0.16. 

2.  16.         5.  400.        8.  TV         11.  0.04.          14.  2500. 

3.  £.  6.  4.  9.  jg.         12.  0.36.  15.  6400. 

16.  What  are  the  two  equal  factors  of  144  ? 

17.  What  are  the  two  equal  factors  of  196  ? 

18.  What  is  that  number  which  multiplied  by  itself  is 
equal  to  121? 

19.  The  square  root  of  130  lies  between  what  two  integers  ? 

20.  The  square  root  of  a  number  between  100  and  10,000 
lies  between  what  two  powers  of  10? 

74.  Square  Root 

Find  the  sides  of  squares  whose  areas  are  as  folloivs  : 

1.  9  sq.  ft.  4.  25  sq.  ft.  7.  Ti^  sq.  in. 

2.  4  sq.  in.  5.  0.04  sq.  in.  8.  2500  sq.  in. 

3.  16  sq.  mi.  6.  4900  sq.  in.          9.  6400  sq.  ft. 

Find  the  perimeters  of  squares  whose  areas  are  : 

10.  TV  sq.  ft.          12.  0.25  sq.  in.         14.  8100  sq.  ft. 

11.  2^  sq.  in.          13.  0.49  sq.  ft.         15.  3600  sq.  yd. 

16.  A  square  floor  has  an  area  of  25  sq.  yd.    Find  its  side. 

17.  A  square  lot  has  an  area  of  14,400  sq.  ft.    How  long 
is  each  side  ?    How  long  is  the  perimeter  ? 

18.  A  square  flower  bed  in  a  park  has  an  area  of  12,100 
sq.  ft.    What  is  each  side  ?    What  is  the  perimeter  ?    How 
does  the  area  compare  with  that  of  a  rectangle  of  the  same 
perimeter  but  100  ft.  wide  ? 


204  POWERS  AND  ROOTS 

75.   Square  Root 

The  square  on  the  hypotenuse  of  a  right  triangle  equals  the 
sum  of  the  squares  on  the  other  two  sides.    Thus  in  this  triangle 
92  +  122  =  152,  for  81  +  144  =  225.   So  if  AB  and 
AC  are  known,  BC  =  V^.J52  +  AC2. 

1.  How  long  is  the  hypotenuse  of  a  right 
triangle  whose  other  sides  are  3  in.  and  4  in.  ? 

2.  How  long  is  the  hypotenuse  of  a  right 

^j.          1«          B 

triangle  whose  other  sides  are  G  ft.  and  8  ft.  ? 

3.  How  long  is  the  hypotenuse  of  a  right  triangle  whose 
other  sides  are  5  ft.  and  12  ft.  ? 

4.  One  side  of  a  right  triangle  is  9  ft.,  and  the  other  is 
33;\-%  longer.    Required  the  length  of  the  hypotenuse. 

5.  How  long  is  the  hypotenuse  of  a  right  triangle  whose 
other  sides  are  \    in.  and  2  in.? 


76.   Square  Root 

1.  The  hypotenuse  is,  5  ft.  and  one  other  side  is  4  ft. 
Required  the  third  side.    • 

2.  The  hypotenuse  is  10  ft.  and  one  other  side  is  6  ft. 
Required  the  third  side. 

3.  The  hypotenuse  is  15  ft.  and  one  other  side  is  12  ft. 
Required  the  other  side. 

4.  The  hypotenuse  is  13  ft.  and  one  other  side  is  12  ft. 
Required  the  third  side. 

5.  What  is  the  'square  of  25  and  also  the  square  root 
of  25? 

6.  State  some  number  less  than  10  whose  square  equals 
its  square  root. 

7.  A  ladder  20  ft.  long  just  reaches  the  sill  of  a  window 
16  ft.  from  the  ground.    How  far  from  the  house  is  the  foot 
of  the  ladder  ?    (162  =  256.) 


CUBE  ROOT  205 

77.   Cube  Root 

To  find  the  cube  root  of  27,000  mentally,  separate  it  into  3  groups 
of  factors,  thus  :  27,000  =  (10  x  3)  x  (10  x  3)  x  (10  x  3)  =  303. 

Find  the  cube  roots  of  the  following  : 

1.  27.       3.  ?\,      5.  1000.          7.  TTJW       9-  Hf 

2.  64.       4.  ^.       6.  64,000.      8.  T|5.       10.  1,000,000. 

11.  What  is  the  edge  of  a  cube  that  contains  125  cu.  in.? 

12.  A  tank  that  is  6  ft.  long,  3  ft.  wide,  and  1  ft.  6  in. 
deep  is  filled  with  water.    This  water  is  then  emptied  into 
a  cubical  tank  and  exactly  fills  it.    What  is  the  edge  of  the 
cubical  tank? 

13.  What  is  the  edge  of  a  cube  that  has  the  same  volume 
as  a  box  that  is  8  in.  long,  4  in.  wide,  and  2  in.  deep  ?  of 
a  box  that  is  10  in.  by  5  in.  by  2£  in.  ? 

78.   Review  of  Roots 

1.  What  is  the  side  of  the  square  that  has  the  same  area 
as  a  rectangle  that  is  4  in.  by  16  in.  ? 

2.  What  is  the  perimeter  of  the  square  that  has  the  same 
area  as  a  rectangle  that  is  3  in.  by  27  in.? 

3.  A  cube  contains  27  cu.  in.    How  many  square  jnches 
in  its  entire  surf a«e  ?  ,  « 

4.  The  entire  surface  of  a  cube  is  96  sq.  in.    What  is  the 
area  of  each  face  ?  the  length  of  each  edge  ?  the  volume  ? 

5.  The  volume  of  a  cube  is  1  cu.  in.    What  is.  the  length 
of  each  edge  ?  the  area  of  each  face  ?   the  entire  surface  ? 
the  combined  length  of  all  the  edges  ? 

6.  A  tank  25  ft.  long,  5  ft.  wide,  and  1  ft.  deep  has  the 
same  capacity  as  a  certain  cubical  tank.    This  cubical  tank 
is  lined  on  four  sides  and  on  the  bottom  with  sheet  lead. 
How  many  square  feet  of  sheet  lead  are  required  to  line  it  ? 


206  MENSURATION 

VIII.   MENSURATION 

79.    Squares 
Find  the  areas  of  squares  with  sides  as  given  : 

1.  11  in.          4.  40  in.  7.  2  ft.  6  in.    10.  3  ft.  4  in. 

2.  15  in.          5.  1$.  ft.  8.  10  ch.         11.  3  yd.  1  ft. 

3.  25  in.  6.  1  ft.  6  in.      9.  20  ch.         12.  100  ft. 

Find  the  sides  of  squares  with  areas  as  given  : 

13.  10  acres.    14.  40  acres.    15.  36  sq.  mi.    16.  144  sq.  rd. 

17.  Find  the  side  of  a  square  whose  area  is  900  sq.  ft. 

18.  How  many  inches  in  the  side  of  a  square  whose  area 
is  1  sq.  ft.  25  sq.  in.  ? 

19.  How  many  feet  in  the  perimeter  of  a  square  whose 
area  is  2  sq.  yd.  7  sq.  ft.  ? 

80.   Rectangles 

Find  the  areas  of  rectangles  with  dimensions  as  given  : 

1.  5  ft.,  37  ft.          4.  8  ft.,  61  ft.  7.  7  yd.,  34  yd. 

2.  6  in.,  42  in.         5.  9  rd.,  23  rd.          8.  4  rd.,  80  rd. 

3.  2  ft.,  3£  ft.          6.  3  ft.,  24  ft.  9.  6  ft.,  7  ft.  2  in. 

Find  the  bases  of  rectangles  with  areas  and  altitudes  as 
given  : 

10.  144  sq.  in.,  6  in.          13.  639  sq.  in.,  9  in. 

11.  135  sq.  ft.,  9  ft.  14.  2  sq.  yd.  2  sq.  ft.,  1  yd.  1  ft. 

12.  510  sq.  in.,  3  in.          15.  65  sq.  in.,  1  ft.  1  in. 

16.  What  is  the  perimeter  of  a  rectangle  9  in.  by  16  in., 
and  of  a  square  of  the  same  area  ? 

17.  A  rectangle  40  ft.  long  has  the  same  area  as  a  square 
20  ft.  on  a  side.    What  is  the  width  of  the  rectangle  ?  How 
does  its  perimeter  compare  with  that  of  the  square  ? 


PARALLELOGRAMS  AXD  TRIANGLES  207 

81.   Parallelograms 

If  a  rectangle  is  2  ft.  1  in.  long  and  4  in.  wide,  its  area  is  4  x  25 
sq.  in.,  or  100  sq.  in.  The  area  of  a  parallelogram  is  equal  to  the  area 
of  a  rectangle  of  the  same  base  and  altitude. 

Find  the  areas  of  parallelograms  with  bases  and  altitudes 
as  given,  using  the  most  convenient  unit: 

1.  1  ft.  1  in.,  1  ft.  1  in.        4.  1  rd.  13^  ft.,  20  ft. 

2.  1  yd.  2  ft.,  1  yd.  1  ft.       5.  1  yd.  4  in.,  11  in. 

3.  1  rd.  3£  ft.,  10  ft.  6.  2  yd.  8  in.,  25  in. 

Find  the  bases  of  parallelograms  with  areas  and  altitudes 
as  given: 

7.  5  sq.  yd.  5  sq.  ft.,  5  ft.    10.  3  sq.  yd.  8  sq.  ft.,  1  yd.  2  ft. 

8.  2  sq.  yd.  2  sq.  ft,  2  ft.     11.  1  sq.  ft.  6  sq.  in.,  10  in. 

9.  Isq.yd.  1  sq.ft.,24in.    12.  1  sq.  ft.  56sq.in.,l  ft. 3  in. 

82.   Triangles 

The  area  of  a  triangle  is  equal  to  half  the  area  of  a  rectangle  of  the 
same  base  and  altitude. 

Find  the  areas  of  triangles  with  bases  and  altitudes  as  given, 
using  the  most  convenient  unit: 

1.  1  ft.  8  in.,  1  ft.  4.  1  yd.  1  ft.,  10  in. 

2.  2  ft.  6  in.,  6  in.  5.  1  rd.  3£  ft.,  6  in. 

3.  3  ft.  4  in.,  8  in.  6.  1  yd.  14  in.,  1  ft.  8  in. 

Find  the  bases  of  triangles  with  areas  and  altitudes  as 
given: 

7.  288  sq.  in.,  1  ft.  10.  630  sq.  in.,  7  in. 

8.  165  sq.  ft.,  1  rd.  11.  810  sq.  ft.,  3  yd. 

9.  640  sq.  in.,  8  in.  12.  1  sq.  yd.  3  sq.  ft.,  1  yd. 
13.  The  hypotenuse  of  a  right  triangle  is  10  in.  and  one 

of  the  other  sides  is  6  in.    What  is  the  third  side  ? 


208  MENSURATION 

83.  Circles 

The  circumference  of  a  circle  equals  2  x  3}  x  the  radius,  or  3£  x  the 
diameter,  nearly.  For  nearer  approximations  mathematicians  use 
3.14159  or  3.1416  instead  of  3i,  but  for  mental  work  3}  or  272  should 
be  used. 

Find  the  circumferences  of  circles  with  these  diameters: 

1.  7  in.  3.  21  in.  5.  210  in.  7.  420  in. 

2.  14  in.  4.  56  in.  6.  350  in.  8.  0.35  in. 
9.  What  is  the  circumference  of  a  water  pipe  that  is  7  in. 

in  diameter  ? 

10.  What  is  the  circumference  of  a  water  tank  that  is 
49  ft.  in  diameter  ? 

11.  What  is  the  circumference  of  a  circular  tent  that 
is  7  ft.  across  ?    14  ft.  across  ?    21  ft.  across  ? 

84.  Circles 

Find  the  circumferences  of  circles  with  these  radii: 

1.  7  in.  3.  21  in.  5.  42  in.  7.  56  in. 

2.  14  in.          4.  35  in.  6.  49  in.  8.  63  in. 

9.  If  the  diameter  of  a  circle  is  0.7  in.,  what  is  the 
circumference  ? 

10.  What  is  the  circumference  of  a  circular  flower  bed 
laid  out  with  a  radius  7  ft.  long  ? 

11.  The  radius  of  a  circular  race  track  is  •£%  mi.   How  far 
is  it  around  the  track  ? 

12.  What  is  the  circumference  of  a  circle  whose  diameter 
is  700  ft.  ? 

13.  A  lady  making  a  drawing  for  a  dress  ornament  de- 
scribes a  circle  with  a  pair  of  compasses  the  points  of  which 
are  3£  in.  apart.    How  much  braid  must  she  allow  to  go 
around  the  circle  ? 


CIRCLES  209 

85.  Circles 

The  area  of  a  circle  equals  £  x  the  radius  x  the  circumference ; 
the  area  of  a  circle  also  equals  272-  x  the  square  of  the  radius. 

Find  the  areas  of  circles  with  the  following  radii  and 
circumferences  : 

1.  7  ft.,  44  ft.      2.  0.7  in.,  4.4  in.      3.  0.07  ft.,  0.44  ft. 

Find  the  areas  of  circles  with  the  follow iny  radii: 
4.  1  in.        5.  7  in.        6.  0.7  in.        7.  0.07  ft.        8.  14  in. 
9.  What  is  the  area  of  a  circular  flower  bed  whose  radius 
is  7  ft.  ? 

10.  What  is  the  area  of  the  cross  section  of  a  water  pipe 
1  in.  in  diameter  ? 

11.  What  is  the  radius  of  a  circle  whose  area  is  154  sq.  in.? 

12.  Find  the  circumference  of  a  circle  with  area  154  sq.in. 

86.  Circles 

1.  What  is  the  area  of  the  cross  section  of  a  pipe  that 
has  a  radius  of  fa  ft.? 

2.  What  is  the  circumference  of  a  circular  flower  bed 
that  has  a  radius  of  3  ft.  6  in.? 

3.  What  is  the  area  of  the  flower  bed  of  Ex.  2  ? 

4.  How  long  is  the  equator  on  a  globe  that  is  14  in.  in 
diameter  ? 

5.  What  is  the  area  of  a  small  circular  table  top  that  is 
14  in.  in  diameter  ? 

6.  What  is  the  .area  of  a  circular  flower  bed  that  has  a 
radius  of  2^  yd.? 

7.  The  radius  of  a  circle  is  1  ft.    What  is  the  length  of 
the  circumference  ? 

8.  The  diameter  of  a  circle'  is  fa  ft.  What  is  the  length 
of  the  circumference  ? 


210  MENSURATION 

87.   Cubes 

Find  the  volumes  of  cubes  with  the  following  edges: 

,      1.  4  in.  4.  7  in.  7.  1.2  in. 

2.  5  in.  5.  9  in.  8.  \  in. 

3.  6  in.  6.  12  in.  9.  1  yd.  1  ft. 

Find  the  edges  of  cubes  with  the  following  volumes  : 

10.  8000  cu.  in.         11.  ^  cu.  in.       12.  2  cu.  yd.  10  cu.  ft. 

Find  the  surfaces  of  cubes  with  the  following  volumes: 
13.  8  cu.  ft.  14.  64  cu.  ft.       15.  125  cu.  in. 

16.  The  surface  of  a  cube  is  24  cu.  ft.  What  is  the  volume  ? 

17.  The  inside  of  a  cubical  tank,  but  not  the  top,  is  to  be 
lined  with  zinc.    The  tank  contains  60  gal.    Allowing  7^  gal. 
to  1  cu.  ft.,  how  many  square  feet  of  zinc  will  be  needed  ? 

88.   Rectangular  Solids 

Find  the  volumes  of  rectangular  solids  as  follows  : 

1.  2  ft.,  3  ft.,  4  ft.  6.  7  ft.,  8  ft.,  9  ft. 

2.  3  ft.,  4  ft.,  5  ft.  7.  8  ft.,  9  ft.,  10  ft. 

3.  4  ft.,  5  ft.,  6  ft.  8.  9  ft.,  10  ft.,  11  ft. 

4.  5  ft.,  6  ft.,  7  ft.  9.  2  ft.,  6  in.,  2£  ft. 

5.  6  ft.,  7  ft.,  8  ft.  10.  2  ft.,  10  in.,  5  in. 

Find  the  volumes  of  rectangular  solids  with  bases  and  alti- 
tudes as  follows : 

11.  36  sq.  in.,  7  in.  13.  72  sq.  in.,  9  in. 

12.  48  sq.  in.,  6  in.  14.  81  sq.  in.,  11  in. 

Find  the  altitudes  of  rectangular  solids  with  volumes  and 
bases  as  follows : 

15.  60  cu.  in.,  20  sq.  in.  16.  189  cu.  in.,  63  sq.  in. 


PRISMS  211 

89.   Prisms 

Find  the  volumes  of  prisms  with  bases  and  altitudes  as 

folio  ir  s  : 

1.  78  sq.  in.,  6  in.  5.  100  sq.  in.,  1  ft.  1  in. 

2.  84  sq.  in.,  7  in.  6.  27  sq.  ft.,  1  yd.  1  ft. 

3.  65  sq.  in.,  9  in.  7.  3  sq.  yd.  3  sq.  ft.,  1  yd.  2  ft. 

4.  52  sq.  in.,  11  in.  8.  1  sq.  ft.  6  sq.  in.,  11  in. 
9.  How  many  loads  (cubic  yards)  of  earth  in  an  exca- 
vation 30  ft.  long,  24  ft.  wide,  and  6  ft.  deep  ? 

10.  How  many  cubic  feet  of  air  in  a  schoolroom  30  ft. 
long,  20  ft.  wide,  and  10  ft.  high  ? 

11.  A  building,  100  ft.  high,  on  a  corner  in  a  city  has  a 
base  that  is  a  triangle  100  ft.  on  one  side  and  50  ft.  in 
altitude.    How  many  cubic  feet  of  space  does  it  occupy  ? 

90.   Prisms 

Find  the  bases  of  prisms  with  volumes  and  altitudes  as 
follows  : 

1.  750  cu.  in.,  25  in.  4.  125  cu.  ft.,  12  ft.  6  in. 

2.  825  cu.  in.,  25  in.  5.  20,000  cu.  ft.,  33J  ft. 

3.  200  cu.  ft.,  12£  ft.  6.  23,000  cu.  ft.,  33  ft.  4  in. 

7.  A  prism  with  a  square  base  a  foot  on  a  side  is  8  in. 
higher  than  it  is  thick.    What  is  its  volume  ? 

8.  A  prism  having  a  volume  of  133  cu.  in.  is  7  in.  high. 
How  many  square  inches  in  the  base  ? 

9.  A  prism  having  a  volume  of  6  cu.  ft.  is  1  yd.  high. 
How  many  square  inches  in  the  base  ?  * 

10.  A  prism  that  is  75  in.  high  has  a  volume  3000  cu.  in. 
How  many  square  inches  in  the  base  ? 

11.  A  prism  that  is  48  in.  high  has  a  volume  of  2§  cu.  ft. 
How  many  square  feet  in  the  base? 


212  MENSURATION 

91.  Cylinders 

Find  the  volumes  of  cylinders  with  bases  and  altitudes  as 
follows  : 

1.  11  sq.  in.,  8  in.  5.  43  sq.  in.,  5  in. 

2.  25  sq.  in.,  7  in.  6.  48  sq.  in.,  12^  in. 

3.  30  sq.  in.,  6  in.  7.  63  sq.  in.,  33J  in. 

4.  32  sq.  in.,  9  in.  8.  800  sq.  in.,  75  in. 

9.  What  is  the  volume  of  a  cylindrical  water  tank  with 
base  of  1200  sq.  ft.  and  height  of  40  ft.  ? 

10.  How  many  cubic  inches  of  water  in  a  pipe  50  ft.  long, 
the  area  of  the  interior  cross  section  being  2  sq.  in.  ? 

11.  A  cylindrical  water  tank  has  a  base  of  2000  sq.  ft. 
and  a  height  of  50  ft.    Allowing  1\  gal.  to  1  cu.  ft.,  how 
many  gallons  will  it  contain  ? 

92.  Cylinders 

The  area  of  the  curved  surface  of  a  cylinder  equals  the  product  of 
the  height  and  the  circumference,  all  considered  as  abstract  numbers. 

Find  the  areas  of  the  curved  surfaces  of  cylinders  with 
heights  and  circumferences  as  follows : 

1.  25  in.,  40  in.  5.  16§  in.,  42  in. 

2.  12£  in.,  32  in.  6.  66§  in.,  33  in. 

3.  33^  in.,  96  in.  7.  50  ft.,  124  ft. 

4.  75  in.,  400  in.  8.  37£  ft.,  80  ft. 

9.  A  water  tank  50  ft.  high  and  126  ft.  in  circumference 
is  to  be  painted  on  the  outside.  How  many  square  feet  of 
surface  must  be  covered  ? 

10.  In  Ex.  9  how  many  square  yards  must  be  covered? 

11.  A  tank  25  ft.  high  and  220  ft.  in  circumference  has 
what  diameter  ?    how  many  square  feet  of  curved  surface  ? 
What  is  the  radius  of  the  base  ? 


PYRAMIDS  213 

93.  Pyramids 

The  volume  of  a  pyramid  equals  one  third  the  product  of  its  base 
and  altitude. 

Find  the  volumes  of  pyramids  with  bases  and  altitudes  as 
follows : 

1.  63  sq.  ft.,  7  ft.  5.  81  sq.  yd.,  8  yd. 

2.  90  sq.  in.,  13  in.  6.  84  sq.  yd.,  30  ft. 

3.  72  sq.  ft.,  6  ft.  7.  93  sq.  in.,  9  in. 

4.  69  sq.  in.,  9  in.  8.  810  sq.  ft.,  12  yd. 

9.  If  the  base  of  a  pyramid  is  a  square  3  yd.  on  a  side, 
and  if  the  pyramid  is  3  ft.  high,  what  is  the  volume  ?  What 
would  the  volume  be  if  the  pyramid  was  3  yd.  high  ? 

10.  The  base  of  a  pyramid  is  a  right  triangle  whose  sides 
are  6  in.,  8  in.,  and  10  in.,  and  the  altitude  of  the  pyramid 
equals  the  hypotenuse  of  the  base.  What  is  the  volume  ? 

94.  Pyramids 

Find  the  bases  of  pyramids  with  volumes  and  altitudes  as 
follows : 

1.  50  cu.  ft.,  5  ft.  5.  48  cu.  yd.,  4  yd. 

2.  36  cu.  ft.,  4  ft.  6.  34  cu.  in.,  2  in. 

3.  60  cu.  ft.,  5  ft.  7.  124  cu.  in.,  4  in. 

4.  70  cu.  ft.,  5  ft.  8.  200  cu.  in.,  10  in. 

Find  the  altitudes  of  pyramids  with  volumes  and  bases  as 
follows : 

9.  220  cu.  in.,  22  sq.  in.       11.  1050  cu.  in.,  210  sq.  in. 
10.  750  cu.  in.,  75  sq.  in.       12.  510  cu.  in.,  170  sq.  in. 

13.  A  pyramid  with  a  triangular  base  has  each  of  its 
edges  7  in.  long.    What  is  the  sum  of  the  -edges  ? 

14.  If  the  base  of  a  pyramid  is  a  square  and  if  the  pyra- 
mid is  10  in.  high  and  has  a  volume  of  30  cu.  in.,  how  long 
is  each  side  of  the  base  ? 


214  MENSURATION 

95.  Cones 

The  volume  of  a  cone  equals  one  third  the  product  of  its  base  and 
altitude. 

Find  the  volumes  of  cones  with  bases  and  altitudes  as 
follows : 

1.  30  sq.  in.,  7  in.  4.  48  sq.  in.,  2^  in. 

2.  36  sq.  in.,  8  in.  5.  60  sq.  in.,  1\  in. 

3.  42  sq.  in.,  6  in.  6.  90  sq.  in.,  15  in. 

Find  the  altitudes  of  cones  with  volumes  and  bases  as 
follows : 

7.  90  cu.  ft.,  30  sq.  ft.  9.  30  cu.  ft.,  30  sq.  ft. 

8.  100  cu.  ft.,  30  sq.  ft.  10.  125  cu.  ft.,  25  sq.  ft. 
11.  A  conical  pile  of  dirt  covers  a  base  of  54  sq.  ft.    It  is 

3  ft.  high.    How  many  loads  (cubic  yards)  does  it  contain  ? 

96.  Cones 

The  lateral  area  (curved  surface)  of  a  right  circular  cone  equals  the 
circumference  of  the  base  multiplied  by  half  of  the  slant  height. 

Find  the  lateral  areas  of  right  circular  cones  with  circum- 
ferences and  slant  heights  as  follows  : 

1.  33  in.,  8  in.        4.  30  in.,  10£  in.        7.  75  in.,  24  in. 

2.  37  in.,  8  in.        5.  40  in.,  12  in.          8.  33  J  in.,  9  in. 

3.  28  in.,  9  in.        6.  50  in.,  1  ft.  9.  32  in.,  12£  in. 

10.  A  cone  has  a  lateral  area  of  217  sq.  in.    The  slant 
height  is  7  in.    What  is  the  circumference  of  the  base  ? 

11.  A  certain  cone  has  a  circular  base  whose  radius  is  7  in. 
The  altitude  of  the  cone  is  30  in.    What  is  the  area  of  the 
base  ?    What  is  the  volume  of  the  cone  ? 

12.  A  paper  cornucopia  has  an  altitude  of  9  in.    The  area 
of  the  open  top  is  6|  sq.  in.    What  is  the  volume  ?    What 
would  be  the  volume  if  the  altitude  was  3  in.? 


SPHERES  215 

97.  Spheres 

The  area  of  a  sphere  equals  4  x  y  x  the  square  of  the  radius. 
Find  the  areas  of  spheres  with  radii  as  follows : 

1.  1  in.  3.  0.1  in.  5.  \  in. 

2.  7  in.  4.   \  in.  6.  0.7  in. 

The  volume  of  a  sphere  equals  f  x  -272  x  the  cube  of  the  radius. 

Find  as  fractions,  without  reducing,  the  volumes  of  spheres 
with  radii  as  follows : 

7.  1  in.  8.  10  in.  9.  0.1  in. 

10.  The  diameter  of  one  sphere  is  1  in.  and  the  diameter 
of  another  sphere  is  2  in.  How  do  the  surfaces  compare? 
How  do  the  volumes  compare  ? 

98.  Review 

1.  If  a  cubic  foot  of  granite  weighs  165  lb.,  what  is  the 
weight  of  a  block  5  ft.  long,  and  2  ft.  square  on  the  end  ? 

2.  If  a  kettle  is  in  the  form  of  a  hemisphere  with  radius 
of  1  ft.,  how  many  cubic  feet  does  it  contain  ? 

3.  If  a  cubic  foot  of  water  weighs  62^  lb.,  what  will  be 
the  weight  of  water  necessary  to  fill  a  cylindrical  tank  2  ft. 
6  in.  high,  the  base  being  4  sq.  ft.  ? 

4.  If  a  cubic  foot  of  marble  weighs  173  lb.,  what  is  the 
weight  of  a  marble  pyramid  whose  base  is  a  square  3  ft.  on 
a  side  and  whose  height  is  3  ft.  4  in.  ? 

5.  If  a  ball  2  in.  in  diameter  has  an  area  of  12^  sq.  in., 
what  is  the  area  of  a  ball  4  in.  in  diameter  ? 

6.  If  a  ball  2  in.  in  diameter  has  a  volume  of  454T  cu.  in., 
what  is  the  volume  of  a  ball  4  in   in  diameter  ?    If  you 
double  the  diameter,  what  effect  does  this  have   on  the 
volume  ? 


216  REVIEW 

99.   Review 

1.  If  8  notebooks  cost  $1.04,  what  does  1  book  cost? 

2.  If  9  Ib.  of  walnuts  cost  $1.62,  what  does  1  Ib.  cost? 

3.  What  do  6  doz.  rulers  cost  at  55/  a  dozen  ? 

4.  Multiply  1640  by  25  in  the  shortest  way. 

5.  The  three  sides  of  a  triangular  lot  are  128  ft.,  140  ft., 
120  ft.    What  is  the  perimeter  ? 

6.  The  four  sides  of  a  quadrilateral  field  are  540  ft., 
460  ft.,  350  ft.,  450  ft.    What  is  the  perimeter  ? 

7.  The  Danube  is  1750  mi.  long  and  the  Ehine  960  mi. 
long.    How  much  longer  is  the  Danube  than  the  Ehine  ? 

8.  What  will   a  railway  ticket  for  148  mi.  cost  at  2/ 
a  mile  ? 

9.  If  7  boys  can  pull  665  Ib.,  what  is  the  average  pull  ? 

100.   Review 

1.  The  product  of  two  numbers  is  156  and  one  of  them 
is  12.    What  is  the  other  number  ? 

2.  The  sum  of  two  numbers  is  341  and  one  of  them  is 
107.    What  is  the  other  number  ? 

3.  The  quotient  of  two  numbers  is  10  and  one  of  them 
is  40.    The  other  may  be  either  of  what  two  numbers  ? 

4.  The  difference  between  two  numbers  is  10  and  one 
of   them   is  34.    The  other  may  be  either  of  what  two 
numbers  ? 

5.  Can  a  line  1  ft.  long  be  divided  exactly  into  equal 
lengths  each  §  in.  long  ?   If  so,  how  many  such  lengths 
are  there? 

6.  At  $125  each,  how  much  will  64  horses  cost?    What 
is  the  shortest  way  of  getting  the  result  ? 

7.  At  $375  each,  how  much  will  24  building  lots  cost  ? 
What  is  the  shortest  way  of  getting  the  result  ? 


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